4

Deec-dba tra drreclonsteteth &tthe teladorshioBazed lor ecaterplot tho correlaiion Cloc betweel 239 and amouni exertisa | Posit I nol clnse Cbse Negatvo but clo...

Question

Deec-dba tra drreclonsteteth &tthe teladorshioBazed lor ecaterplot tho correlaiion Cloc betweel 239 and amouni exertisa | Posit I nol clnse Cbse Negatvo but cloza CoeeFind tne value of the correlation cooficst; Cces Uvovo 076e milYou orewerWhat proportion ci tne vadabion nube0 nou& Rar erz aincd %y #94?Find Eezst SCueres fegress 0n Ene fc" predicting numbe 0rnruns 3 D2zon Arnfoas 7or2d teraj8.Lc the mgression equaten 'Preddt that amount = exercie fora Fersen #to 40 years Cd_ at

Deec-dba tra drreclon steteth &tthe teladorshio Bazed lor ecaterplot tho correlaiion Cloc betweel 239 and amouni exertisa | Posit I nol clnse Cbse Negatvo but cloza Coee Find tne value of the correlation cooficst; Cces Uvovo 076e milYou orewer What proportion ci tne vadabion nube0 nou& Rar erz aincd %y #94? Find Eezst SCueres fegress 0n Ene fc" predicting numbe 0rnruns 3 D2zon Arnfoas 7or2d teraj8. Lc the mgression equaten 'Preddt that amount = exercie fora Fersen #to 40 years Cd_ athis valid Fredicton? Vhhy&r Myrcn Uza ma regtession equabon predic (he amount cf exercsc fcr a person Wo 14Yezn cice Lhls a valid predlcton? Why My1 True €r Felse? Bace trere Fant} stong cone ulu Nc cn craude that Icreescd 2ce Catarl pepen t0 exercie 683 EpaML whot should we do # we want ta etloblth covtatlon (Ihall increased 0g0 coutOs Daton Ereicce (U8i8



Answers

Use the data in HTV for this exercise.
(i) Run a simple OLS regression on educ. Without controlling for other factors, what
is the 95$\%$ confidence interval for the return to another year of education?
(ii) The variable ctuit, in thousands of dollars, is the change in college tuition facing students from
age 17 to age $18 .$ Show that $e d u c$ and ctuit are essentially uncorrelated. What does this say
about ctuit as a possible IV for educ in a simple regression analysis?
(iii) Now, add to the simple regression model in part (i) a quadratic in experience and a full set of
regional dummy variables for current residence and residence at age $18 .$ Also include the urban
indicators for current and age 18 residences. What is the estimated return to a year of education?
(iv) Again using ctuit as a potential IV for educ, estimate the reduced form for educ. [Naturally, the
reduced form for educ now includes the explanatory variables in part (iii).] Show that ctuit is
now statistically significant in the reduced form for educ.
(v) Estimate the model from part (ii) by IV, using ctuit as an IV for educ. How does the confidence
interval for the return to education compare with the OLS CI from part (iii)?
(vi) Do you think the IV procedure from part (v) is convincing?

Apartment. The size of the sample is 7000 430 students. The percentage of students attending a catholic high school is six 0.1 percent. Now you can find this number by this function in. Are you into summary the data? Said catholic a dollar sign and are variable of interest catholic high school. And this number is the mean of the variable to see exactly how many students attending catholic high school. You can either multiply 6.1% with the total number of students or you can use this variable um tablet generated from function table. You will find that there are only 452 students going to catholic high schools, aren't you? This is the regression result using A. S. We have beta one. The estimate on catholic high school attendance here 1.48 with a centered barrel of point for two. So this estimate is highly significant to find the 95% confidence interval. You can either go with their formula, which means you have to look up their critical value. Or you can use in our you can use this function on event and you can put the name of the regression in it. This function will return the 95% confidence interval for all variables in their regression. And the interval is yeah 0.658 Running to you. 2.297 part three. We use variable power cast as an instrument for calf H. S. Yeah, this variable Parkas takes a value of one if a parent reports being catholic and the problem asked you to estimate the reduced form which means you win the regress the endogenous variable catholic high school on the instrument and other exhaustion. Ist variables in the right hand side of the structural equation, there are two other exogenous variables. Mother education, father education should be more and family income, so you should have four variables on the right hand side introduced form equation. The estimate on Park F. Is Poin on four and the T value is 25.7. So this variable is uh large and significant and relevant. So it it would be a good instrument, assuming that this variable does not correlate with the error terms in the structural equation. Okay, we will come back to the equation in part three and we estimate it again with instrument variable. This is a result. Is this better one? So all the estimates are significant compared to you what we get in part three. The instrument variable approach produced an estimate for beta one that is four times greater than the old L. S estimate. Yeah, the 95% confidence interval is now on 0.244 Upper limit is 6.991 Yeah this is a wider range which makes sense because the standard error in the ivy approach is larger and there is a slight overlap between the two confidence intervals. Okay. Past five. You in tests another hypothesis that catholic high school variable is exogenous and what you can do is to follow sections 50 teen 0.5. In the textbook first you can obtain the residuals from the reduced form regression. You will include the residuals in the structural equation, meaning you in regress math 12 on catholic high school. The suspected indulge in is variable and other exogenous variable except the I. V. I get the coefficient on the residual to b minus 2.8 75 With a centered era of 1.5 to 6. That gives me a T. Value of minus 1.885 and a p value of one oh six. We are able to sir, we are unable to reject the non hypothesis that the coefficient or the estimate on residual is not different. Steve it's not different from zero. This non hypothesis is equivalent debt equivalent here. Um catholic high school is exogenous. So at the 5% confidence level we can um believe that catholic high school is endogenous. Our sixth. You add the interaction between catholic high school and mother education to the above model. It is in general endogenous because because catholic high school is endogenous, so any interaction term of it is likely endogenous and the next question is likely to have a typo there is no parent education in the data set and this variable is not mentioned any further in the problem, the correct one should be parent catholic. So because parent catholic is a good instrument for catholic high school attendance, we expect the interaction between parents catholic and mother education to be good. A good instrument for the interaction between Catholics high school and mother education. In part seven we add an interaction term to the equation and I find the estimate on it to be minus four point 881 with a centered errol of one point 084 That gives me a T. Value of minus 4.5. So this term is highly significant. Mark eight. Mhm. I find that including the interaction term important for estimating the average partial effect. The average pasture effect of a variable in our can be found from this function margins and to show the centre errol of this martian estimate. Mhm. Along with the p value, you will need summary function outside this margin function. I find the average partial estimate uh effect of catholic high school in the new re question to be seven points 448 with a standard barrel over one point triple eight. The T value is 3.94 and the p value is almost zero. So this effect, the effect of attending catholic high school is stronger and more significant.

Part one. The Poland L s estimate of beta one oh is 0.36 zero. If the change in concentrate concentration is 0.1, then the change in the log of fair would be Beijing one head times the change in concentration and that would be 0.36 times 0.1, which is 0.36 That implies airfare is estimated to be about 3.6% higher. Part two, The 95% confidence interval obtain using the usual L s standard error is 0.301 2.419 And if we use the fully robust standard Iran's we will get point 245 and 2450.475 which is wider than the one above. The wider confidence interval is appropriate as the neglected serial correlation introduced uncertainty into our parameter estimation. Yeah, Part three. The quadratic has a use shape form, and the turning point is calculated by mhm taking partial derivative of lock of airfare with respect to lock of distance. And you will set that derivative equal zero. You wouldn't be able to find the value of lack of distance where the slope becomes positive, sir. the value of a lot of distance at the turning point is you will take 0.902 divided by two times 20.103 and you can get 4.38 This is the lock of distance, sir. When you convert it back, the value of distance is exponential of 4.38 Okay, about 80. And the shortest distance in the sample is 95 miles. So the turning point is outside the range of the data, which is a good thing in this case, what is being captured in an increasing elasticity affair with respect your distance As fare increases hard for the random effect, estimate of data one is 10.209 which is a bit smaller than the parent LS estimate. This estimate still implies a positive relationship between fair and concentration. The estimate is also very significant, with a T statistic of 7.88 Part five. The fixed effects estimate of beta one is 10.169 which is lower but not so different from the random effect estimate. And this is so because the value of, um, a perimeter in Equation 11 equation 14.11. Yeah, let's say it's, um, Fate. A hat. The Fed ahead is about 0.9, so random effects and fixed effects as meats are fairly similar. Remember, random effect uses a quasi demeaning. That depends on the estimate of this fada, I suggest in equation 14.11. Hard six. Heterogeneous effect. A supply could capture two types of factors that might correlate with concentration. Variable mhm. First, it could be factors about cities mhm near the two airports, for example, population, education level and type of employers. These factors could affect the demand for air travel, and the second set of factors could be factors relate you geographical features and infrastructure condition, such as highway qualities and whether the city locates near a river. So these factors are able to change over time. But in a short time period, let's say, um, the length of the time study in their sample. They are roughly time constant course, Yeah, and so they are able to be captured by a sub I. There are various factors like that, and it's better if we are able to control for them. So in part seven, it is more appropriate to choose to fix effect, estimate

All right. Hello, everybody. Today we're gonna be doing some more modeling. So first things first. As always. You want to make sure you have be Wooldridge package installed. This package contains all the data, and then you want to just select the world rich library. Make sure we're using that. Um, we're gonna be using one equation or one. We're gonna be referencing one previous equation. That's gonna be log wage. Actually, it's gonna be L wage, as it's referred to in the data set, is equal to base Eclipse University experience. It's good to have that written down. So we can for back to it. And all right, let's get started. So first, we're talking about the S total variable, which refers to standardize test total, and it's a proxy variable for un observed abilities are first thing we want to do is we want to find our sample mean and standard deviation we were going to do that is very simply that the data set So our data set is two year that will select that one of you two year weaken. View that now, over here, you can see all these different things. If I scroll you will see you know, the various different categories. So, um, to find the mean and standard deviation Very easy function. We're just gonna take the mean off the S total column in two years. And then we're gonna take the standard deviation of the S total column into your perfect right there very quickly. We have our mean and rest and deviation. So now we want to run some basic aggressions. We want to run a regression of J. C. On s total and of university on a So and we want to find out, Are they statistically related? So that's pretty simple. We're gonna say R J c regression is gonna be a linear model, right? And it's very simply, our formula is just gonna be that of J. C on total Y on X obviously referencing the two year data set and then our university regression is gonna be the exact same bring. But instead of J. C, we're gonna write university. And then again, Data said, he's I think the summary of these JC wreg and summary of you know right you will see for a J. C wreg Um, thes s total is not statistically significant, right? It's 0.31 You will also see for university, however, is statistically significant. Um, you can see that from the three Asterix here, showing its significant at the 30.1% confidence level. So it's obviously a significant at five or also from the fact that our probability is less than two times sentenced to 16. So Okay, um, it is statistically significant in determining university, but not J. C. All right, cool. So now we want Teoh. Now we want Teoh take our equation from before up here This l wage Ah, um, to J C University and Experience. And we want to add s total into that. So are primary model is going to be lm Elway's being C plus university puts experience, and now we're gonna add in as total our data state is still two year. When we take the summary of our primary model, you will get this again notice Everything is significant at the five and also at the 50.1% confidence levels. But there seems to be no real difference in the conclusion drawn because, um, you know, both JC and university are still statistically significant with or without s total in the model. And if you want me toe, really click do that. I can actually just do summary of l m l. Wage Juicy plus university experience. Data equals two year. You can see that even without, um as total all of these air still statistically signify Right. Okay, Cool. So, um, now we want to test the hypothesis that the returns are these same against the alternative that the return toe four year colleges greater. So there are a few of doing a few ways of doing this. The one I like is actually a little method where our formula will change to make our lives easier. So instead of saying J C plus university plus experience plus esto, we're gonna have J. C. Plus, uh, let me check the column name again. Just a warning. So you'll see. We have Ah, somewhere in here we should have. Yeah, we have a variable called Total College, which basically adds together R J c. And our university, right? The number of years and that variable combines those two variables. So if we want, say so, if our, um no hypothesis is B one equal to be too right where B one is The coefficient for J. C. B two is equal to university and our alternative hypothesis I mean, start commenting. Visit are all turned. This hypothesis is B one is less than right. Weaken Ben, rewrite this, as are no hypothesis being the one minus B two equals zero and you one minus beat you is lessons here. Now, Now, if we put these if we combine be one minus B two into one variable. Right? Um so basically, what we can do is we can change our equation around and instead of, um saying J C plus University, right, with two separate variables, we make a J C plus total college, and then the coefficient for J. C will be This represent will represent the one minus B two because we'll take out everything that's B two, and we'll tack it on to university with the total college. Very, it's a little bit confusing, but it's, um it's my preferred method for doing these multi, um, multi variable hypotheses. So basically our new model, it's going to be lm l Wage is going to J C plus tote call used at the right variable name I almost forgot. Yeah. J C plus toe call plus experience. Plus s total. Dana equals two year. And then if we take a summary of our new model, we will find that J. C is no longer statistically significant, Which means that we that we reject the alternative hypothesis. We're sorry we don't reject the alternative hypothesis. We failed to reject the null hypothesis, which is that there is, um no diff. So, yes, there does seem to be no difference in the conclusion drawn between two year and four year colleges, with or without s total in the model. We know that without from before Okay, that was a doozy. Let's just run through this one more time. Really Quick. We have are null hypothesis B one equals B to basically saying that you have these two j. C. And university or the same. We we've rearranged our equation, so we only have to account for one variable, essentially read or not equals zero vs Straight on. Not is less than zero. Right, And we find So this is they don't not. We find that our probability here is point for 21 which means that there is no statistical significance. We failed to reject the null hypothesis. And, um, that there isn't a difference essentially between two and four year colleges. Okay. You all right? So now we're gonna, um we're going toe Ask for our equation from here. Sorry. No for equation here. We added s total up here, right? Same equation. Added Estelle. Now we're asking, Do we require quadratic for this equation? So our model squared, right? Just doing in that quarter at it is gonna be l wage. They see, plus university plus experience plus s total and now are quadratic. Um, very well, we're gonna write I as total squid. You need the eye to make sure that, um that the formula reads as you squaring it and not doing something else. We're because our is a funny language. All right. When I take this summary of this model, I will find that this is not statistically significant at all. It's probabilities 0.69 and that's not statistically significant at the 5% confidence of were really any reasonable confidence level. So we don't require a quadratic variable to determine l wage. Okay. Now, um, we want to add the now we want to try the same thing again, right? We want to add something and see if it's necessary. But we're gonna try with the interaction terms as total times, J C and s Total Times University. So we're gonna try it with those interaction terms and see if the mob, if they're jointly significant now, joint significance is a bit different. And I'll explain that in a second. So our model interact right with our interaction crimes always J c University experience as total. And then we're gonna have as total times J. C and S Total Tang's University agreed A is going to be two years. All right. Summary of this model. Oh, yeah. You can say from here that Oh, neither of these are statistically significant of 5%. But that doesn't actually give you their joint significance that gives you the individual significance is of these to get the joint significance. What we're gonna do is we're in use a function called a nova. We're gonna put our restricted modeled first. That's the primary model. Then we're gonna put our unrestricted model second. That's our interaction. Well, if we want this ucr degrees of freedom decreased by two makes sense because we added in two more terms, and our probability of this happening is tweet one for one. Now, since the P value of this is an F statistic, right, that's all this is, since the P value of R F statistic is greater than, um, the critical P value of 0.5 right, which is our 5% significant several since is greater than that. Both of the interaction terms are jointly statistically insignificant at the 5% level between both of them can get thrown out. So our final model that controls for will be using s total is going to be not right. This here, the log away equals, and I'm gonna read this with the intercepts, so be no. That's our intercept. Plus B one J c. Must be to university again. Those are just coefficients. B three experience was be for s total. Plus, are you for error? That is going to be the final equation. We use Teoh make our model controlling for, um ability. All right. And that's all. Thank you very much. Have a good day


Similar Solved Questions

5 answers
Reproduced with permission from Sigma-Aldrich Co. LLC100 9060 50 1 40 30 20 1014 13 12 11 108 7 5 4 Chemical Shift (0) ppm2 1-1 - -3 - -Zoom In Click and drag over part or the whole spectrum Zoom Out - Double-click on anv nart of the spectrum
Reproduced with permission from Sigma-Aldrich Co. LLC 100 90 60 50 1 40 30 20 10 14 13 12 11 10 8 7 5 4 Chemical Shift (0) ppm 2 1 -1 - -3 - - Zoom In Click and drag over part or the whole spectrum Zoom Out - Double-click on anv nart of the spectrum...
5 answers
21Consider the amino acid arginine, shown below with the relevant pKa values:9.12 NHz-0.54IHzN_OH 2.41NH2.41What is the isoelectric point for this amino acid?
21 Consider the amino acid arginine, shown below with the relevant pKa values: 9.12 NHz -0.54 I HzN_ OH 2.41 NH 2.41 What is the isoelectric point for this amino acid?...
5 answers
A solution is made by mixing 09. g of acetyl bromide (CH,COBr) and 70. g of thiophene (CAH4S): Calculate the mole fraction of acetyl bromide In this solution. Be sure your answer has the correct number of significant digIBet KnowSubmitFaoizeeaWeleeee
A solution is made by mixing 09. g of acetyl bromide (CH,COBr) and 70. g of thiophene (CAH4S): Calculate the mole fraction of acetyl bromide In this solution. Be sure your answer has the correct number of significant dig IBet Know Submit Faoizeea Weleeee...
5 answers
Compare dy and Ay for y - -4x? _ 3 atr=-I with &x = dx = 0.06. Give your answers to four decimal places:dy --0.4900; Ay - -0. 4946 dy --0.5100; Ay --0.4947 dy --0, 4600; 4y = -0,4945 dy = -0. 4800; 4y = -0.4944 dy--0.5100; 4y --0.4945
Compare dy and Ay for y - -4x? _ 3 atr=-I with &x = dx = 0.06. Give your answers to four decimal places: dy --0.4900; Ay - -0. 4946 dy --0.5100; Ay --0.4947 dy --0, 4600; 4y = -0,4945 dy = -0. 4800; 4y = -0.4944 dy--0.5100; 4y --0.4945...
5 answers
Evaluate the integral. (Use C for the constantt6 In(t) dt7in6)/7 17 + ( 49
Evaluate the integral. (Use C for the constant t6 In(t) dt 7in6)/7 17 + ( 49...
5 answers
((3.2 #7) An oblong number counts the numbers of dots in a rectangular array in a rectangular array having one more rOW than it has columns; the first few of these numbers are01 = 2 02 = 6 03 = 12 04 = 20and in general the nth number is given by On = n(n + 1). Prove algebraic and geometrically that On 22 =n
((3.2 #7) An oblong number counts the numbers of dots in a rectangular array in a rectangular array having one more rOW than it has columns; the first few of these numbers are 01 = 2 02 = 6 03 = 12 04 = 20 and in general the nth number is given by On = n(n + 1). Prove algebraic and geometrically tha...
5 answers
Find? Lhe radiug &ud tbe iulerval of couvergence [or lhe following power series5)" n . 3'
Find? Lhe radiug &ud tbe iulerval of couvergence [or lhe following power series 5)" n . 3'...
5 answers
EJqabiv s6u/yl IIV) UOSIIM EUISLC(6 - Xlz)J(l-xL) oqu pue (9 xz) Juu DHa7 slDosiq HJ :UJND '0L(Ez x6)8818~(E [ 491)TJO anie^ 241 puly :suoi13ajia
eJqabiv s6u/yl IIV) UOSIIM EUIS LC (6 - Xlz) J(l-xL) oqu pue (9 xz) Juu DHa7 slDosiq HJ :UJND '0L (Ez x6) 88 18 ~(E [ 491) TJO anie^ 241 puly :suoi13ajia...
1 answers
Evaluate each limit (if it exists). Use L'Hospital's rule (if appropriate). $$\lim _{x \rightarrow 0} \frac{\ln \cos x}{x}$$
Evaluate each limit (if it exists). Use L'Hospital's rule (if appropriate). $$\lim _{x \rightarrow 0} \frac{\ln \cos x}{x}$$...
1 answers
Evaluate the expression, if possible. $$\sqrt{9}$$
Evaluate the expression, if possible. $$\sqrt{9}$$...
5 answers
What is the magnitude of the force on a 20 μC electriccharge located at the origin due to charges q1 andq2 which are located on the x-axis at + 10 cm and -10 cm, respectively. The charge of q1 is 10 μCand q2 is - 10 μC.0.04 N180 N0.02 N0 N360 N
What is the magnitude of the force on a 20 μC electric charge located at the origin due to charges q1 and q2 which are located on the x-axis at + 10 cm and - 10 cm, respectively. The charge of q1 is 10 μC and q2 is - 10 μC. 0.04 N 180 N 0.02 N 0 N 360 N...
5 answers
This Question:10 of 12 (8sin 0 + cos O)( sin Multiply and simplity coscos () -(sin 0 + cos O)( sin 0+ cos 0) sin Ucos (Use integers or fractions for any numbers in the expression )
This Question: 10 of 12 (8 sin 0 + cos O)( sin Multiply and simplity cos cos () - (sin 0 + cos O)( sin 0+ cos 0) sin Ucos (Use integers or fractions for any numbers in the expression )...
5 answers
How is statistical power affected if the effect size of interest(for example, a difference between two treatment groups) in a studyturns out to be larger than what was anticipated?Statistical power is increasedStatistical power is decreasedStatistical power is unchangedIt depends on whether the data are matched or unmatched
How is statistical power affected if the effect size of interest (for example, a difference between two treatment groups) in a study turns out to be larger than what was anticipated? Statistical power is increased Statistical power is decreased Statistical power is unchanged It depends on whether th...
5 answers
Calculate the exact value of the integralJUp % dcdydzwhere D is a pyramid defined by the vertices (-1,-2, 0), (-1,3, 0), (2,1, 0), (3,-1, 0) and (0,0,2)
Calculate the exact value of the integral JUp % dcdydz where D is a pyramid defined by the vertices (-1,-2, 0), (-1,3, 0), (2,1, 0), (3,-1, 0) and (0,0,2)...

-- 0.018999--