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Lastly, run full multiple regression including all of the variables, including teoeyal generated and used in a previous model (mother). Note: the base_group (class ...

Question

Lastly, run full multiple regression including all of the variables, including teoeyal generated and used in a previous model (mother). Note: the base_group (class 3_ should not be_included when Yourun the regression Coefficients Standard Error t Stat P-value P-value Intercept (Survivor) 0.128694691 0.052410724 2.455503004 0.014260306 0.014 X Variable 1 (Mother) 0.20716781 0.061770487 3.353831585 0.000830898 X Variable 2 (Parents) -0.05491435 0.054284612 -1.011600672 0.312005825 0.312 X Variable

Lastly, run full multiple regression including all of the variables, including teoeyal generated and used in a previous model (mother). Note: the base_group (class 3_ should not be_included when Yourun the regression Coefficients Standard Error t Stat P-value P-value Intercept (Survivor) 0.128694691 0.052410724 2.455503004 0.014260306 0.014 X Variable 1 (Mother) 0.20716781 0.061770487 3.353831585 0.000830898 X Variable 2 (Parents) -0.05491435 0.054284612 -1.011600672 0.312005825 0.312 X Variable 3 (Female) 0.368471759 0.052576097 7.008351377 4,78E-12 X Variable 4 (Children) 0.110255939 0.053500614 2.060835033 0.039610833 0.039 X Variable 5 (Class 1) 0.30673288 0.031681264 9.681838288 3.86E-21 X Variable 6 (Class 2) 0.162087524 0.033465692 4.843393751 1,51E-06 Write the specific estimate equation for the model above; including values for coefficients and names for variables. Which of your variables are significant at the 5% level? Also, is your model significant as a whole? Variables that are significant at a 5% level = X Variable 1 (Mother) X Variable 3 (Female) X Variable 4 (Children) X Variable 5 (Class 1) X Variable 6 (Class 2) Our model is significant because the P-values are statistically significant besides the "Parent Variable" Using your model, estimate the likelihood that Mr: Lawrence Beesley (passenger number 22) would_ve survived. Are you surprised he survived? It was not likely that Mr: Lawrence Beesly survived. Males surviving was not likely especially male parents with a P-value of 312_ Summarize your results for this model in three sentences. What impacted someone'$ likelihood of surviving the Titanic crash?



Answers

Use APPLE to verify some of the claims made in Section $6-3$ .
(i) Run the regression ecolbs on ecoprc, regprc and report the results in the usual form, including the $R$ -squared and adjusted $R$ -squared. Interpret the coefficients on the price variables and comment on their signs and magnitudes.
(ii) Are the price variables statistically significant? Report the $p$ -values for the individual tests.
(iii) What is the range of fitted values for ecolbs? What fraction of the sample reports ecolbs = 0?
Comment.
(iv) Do you think the price variables together do a good job of explaining variation in ecolbs? Explain.
(v) Add the variables faminc, hhsize (household size), educ, and age to the regression from part (i). Find the $p$ -value for their joint significance. What do you conclude?
(vi) Run separate simple regressions of ecolbs on ecoprc and then ecolbs on regpre. How do the simple regression coefficients compare with the multiple regression from part (i)? Find the correlation coefficient between ecoprc and regprc to help explain your findings.
(vii) Consider a model that adds family income and the quantity demanded for regular apples:
$e c o l b s=\beta_{0}+\beta_{1} e c o p r c+\beta_{2} r e g p r c+\beta_{3}$ faminc $+\beta_{4} r e g l b s+u$
From basic economic theory, which explanatory variable does not belong to the equation? When you drop the variables one at a time time, do the sizes of the adjusted $R$ -squareds affect your answer?

Part one. The results of the progression are Intercept is 1.9 estimate on Eco Price is -2.9 And the estimate on regular price is 3.03. And all of these estimates are highly significant. The r square is very low point 04 and r squared adjusted has similar value. We have 660 observations in our simple, so the simple is not small at all. This model is just not very good. The problem asks you to interpret the result, so this result is as predicted by economic theory. The own price effect is negative and the cross or substitute price effect is positive. An increase in echo price of 10 sense per pound Reduces the estimated demand for Eco label Apples by about .29. Mhm .29 lbs. An increase in regular price of 10 cents per pound for regular apples increases the estimated demand for eco labelled apples by about 0.3 The unit is pound. These effects are quite large in part two. So as I said earlier, each price bearable is individually significant, with a T statistic Greater than four in absolute value. The P values are essentially zero and we conclude that they are significant. Our tree, the fitted values has a minimum of 0.86 and the maximum of 2.09. This is much smaller range than e cole label pounds. The observed demand itself, Which ranged from 0 to 42, Although 42 is kind of an outlier, There are almost 2 50 observations with estimated no not estimated observed demand for eco label apples being zero and these observations are not accounted for in their predicted values. Our sixth, the r square is about 3.6%. This is very small. The model can only explain 3.6, less than 4% of the variation in the demand for eco label apples. The two price variables do not do a good job of explaining why demand varies across families. Part five. We add family income, household size, education and egg to you. Uh The regression that are square increased U exactly 4% and the adjusted osce square falls from point 0342 points 031 We can test the joint significance of the additional variable and the f statistic with four and 653 degrees of freedom has a P value of 0.63 So we are unable to retract the null hypothesis that the estimate on these variables are jointly uh equally zero or six. The problem asked you to run separate simple regressions of demand on price. Of eco labelled opposed and then demand on regular regular price. Yeah. I find that there are square in both cases to be very small, almost zero. And when you calculate the correlation coefficient between eco price and regular price, you would find The coefficient to be .83. So it is possible that the monte culinary t over these variables affect the fit of the model. In part seven we consider a model that adds family income and the quantity demanded for regular apples from basic economic theory. Okay, the regular the man does not belong to the equation. When we estimate the full model, we get our square of point oh six Adjusted r squared of .57 and we will drop the variables one at the time. So if we drop the price of eco labelled variable are square is .03 and at just the square is point 0 to 5. Then if we drop regular price It's just a square is .039. Oh regular, Our square is .039. It's just our square is .035 family income to be dropped. Our square is .06 at just a square is .056. Drop regular apple demand. Our Square is .038. It's just that our square is point oh 34 and all of these are smaller than there are square and adjusted r squared values from their full model. We conclude that the initial old model is still the best.

In this part, you are going to show some statistics of the variable net F. A thistle variable indicates the Net total financial assets in thousands of dollars. This variable has a mean of 19 up seven. The standard deviation is 63 Boyne Nice six. The minimum level is minus 502.3 and the maximum level is 1000 536 18 Remember, these numbers are in 1000. In the second part, you are going to test whether the average net total asset differs by 401 k eligibility studies and you can use a two sided alternative. The null hypothesis of this question is the average of net S A for their group that is eligible for for one cave equal that f A of the group that is not Elizabeth. For 41 K, we would do a T test and the T test. We will get a value of 13 11 The P value off the test is very small is way smaller than 0.1 So we are able to reject the non hypotheses that two groups have equal net total financial asset. The difference between the two groups in that total financial asset is well intact. The value of Met Toto A set the average one for the group that is eligible for 401 K, which is 30 points 54 These numbers are generated by their statistical software. Then we subtract from it their average net F A of the group that is not eligible for for a one K, which is 11 going 68 What we get is roughly 18 0.86 So the group that is eligible for for one K has a larger average net total financial asset, and it is larger by the average of the groups ineligible for 41 K by 18.8 $6000. We will estimate a mentally near regression model for net total financial assets. That includes income age eligibility for 401 K, and we also have age and income included in the regression as quadratic form. Okay, we will look at the coefficient of the variable E for a one K. As an indicator of the estimated dollar effect of the eligibility status, the coefficient of E 41 k is nine point 705 It means that if the family is illegible 4401 k, their net total financial asset when increased by $9705 we will add to the model estimated in Part three, the interaction terms of a legibility status and age minus 41. And another term is the interaction of eligibility status and age minus 41 square. This is the regression result. When we look at the interaction terms, we see that only this term it's significant. The term with Asian minus 41 the term with Asia minus 41 square, is not significant. In future models, we can safely drop the last term. Women compare the estimated effect of the allege ability status between model in Part three and model in Part four. The left panel show the regression results from the model. In part, we and the right panel show the results from the model. In Part four, you can tell the difference of the coefficient of E 401 K between two models. In monetary, it is 9.75 A model for it is 9.960 You should note that the meaning of the coefficient of E 401 k, the first between two models in model three. It is the effect for all ages. A model for it is the effect when age equals 40. 1 way will include family size dummies In the regression equation, you can see that in our equation we now have F s two s, three s four and fs five. These are their families side dummies F s two takes a value of one if the family has to people access to equal zero otherwise, after three takes a value of one. If the family has three people and takes a value of zero otherwise ever as far is for family of four. And Verse five is for family with more than five people. Mhm. So you don't cfs one in the equation. That is because Fs one or a family of one is the base group We have to base group So all the coefficient of the dummies should be interpreted as the difference in net total asset compared to the base group. So among the four dummies, you can see that Fs two is not significant. F s 32 Fs five are significant and the level of significance of these dummies increases with their size of the families. So have a sweet It's significant at the 5% level. But s four and s wide are significant at the 1% level. Even the P value you can say that compared to the base group, a family of a single person having three or more people in the family associate with a greater average value of net total financial assets. We can also conduct a F test to see the joint significance of their family size dummies. The null hypothesis is the coefficient of the family size dummy equals each other and equals zero. We will get an F statistic with two degrees of freedom four and NYT housing 265. The statistic is 5.44 and the P value it's very, very small is way smaller than 0.1 So we are able to reject the null hypothesis. In other words, the family size dummies are jointly significant. At the 1% level, we will do a child test forward coefficient equality across five family sized categories For the test statistic. We we need some of square residual from the unrestricted models and re restricted model. The restricted model comes from Part six and we use the phone sample to estimated The sum of square residual for the respective model is 30 million yeah, 213,000 and 115 for the and restricted models. They are five of them. They are estimated separately for each category of family size. The sum of square residual for and restricted models is the sum of the sum of square residual of all five models. Adding them up. You wouldn't get a total of 29 million, 980,000 and 959 now. Given that we have there some of square residual for the restricted model and unrestricted models, we can calculate the F statistic or the child test statistic the child has is based on the F distribution. That's why we have an F statistic. This is their formula for the F statistic. We will take the sum of square residual of the restricted model minus the sum of square of residual of the unrestricted model divided by their sum of square of residual of the unrestricted model altogether multiply with the ratio of the second degree of freedom divided by the first degree of freedom. These degrees of freedom are given from their problem. We have D F one. The first degree of freedom is the number of constraints were going to test, which is 20 and the second degrees of freedom is given as NYT housing and 245. The F statistic would be three point 57 and we can back up the P value using your statistical software. It is a very small number 0.0 03 So we are able to reject the null hypotheses at the 1% level, which means the coefficients are not equal across five family size categories.

In this part, you are going to show some statistics of the variable net F. A thistle variable indicates the Net total financial assets in thousands of dollars. This variable has a mean of 19 up seven. The standard deviation is 63 going nice six. The minimum level is minus 502.3 and the maximum level is 1000 536 18 Remember, these numbers are in 1000. In the second part, you are going to test whether the average net total asset differs by 401 k eligibility studies and you can use a two sided alternative. The null hypothesis of this question is the average of net S A for their group that is eligible for for one cave equal that f A of the group that is not eligible for 41 K. We would do a T test and the T test. We will get a value of 13 11 The P value off the test is very small is way smaller than 0.1 So we are able to reject the non hypotheses that two groups have equal net total financial asset. The difference between the two groups in that total financial asset is, well intake. The value of Met Toto A set the average one for the group that is eligible for for a one K, which is 30 points 54 These numbers are generated by their statistical software. Then we subtract from it their average net F A of the group that is not eligible for for a one K, which is 11 going six eight What we get. ISS roughly 18 0.86 mhm. So the group that is eligible for for one K has a larger average net total financial asset, and it is larger by the average of the groups ineligible for 41 K by 18.8 $6000. We will estimate a mentally near regression model for net total financial assets. That includes income age eligibility for 401 K, and we also have age and income included in the regression As quadratic form. We will look at the coefficient of the variable E for a one K as an indicator of the estimated dollar effect of the eligibility status. Can you talk? The coefficient of E 41 K is nine point 705 It means that if the family is Elizabeth 4401 k, their net total financial asset when increased by $9705 we will add to the model estimated in Part three, the interaction terms of a legibility status and H minus 41. And another term is the interaction of eligibility status and age minus 41 square. This is the regression result. When we look at the interaction terms, we see that only this term it's significant. The term with Asian minus 41 the term with Asia minus 41 square, is not significant. In future models, we can safely drop the last term. Women compare the estimated effect of the eligibility status between model in Part three and model in Part four. The left panel show the regression results from the model. In part, we and the right panel show the results from the model. In Part four, you can tell the difference of the coefficient of E 401 K between two models. In monetary, it is 9.705 A model for it is 9.960 You should note that the meaning of the coefficient of e 401 k in first between two models in model three, it is the effect for all ages. A model for it is the effect when age equals 40. 1 way will include family size dummies In the regression equation, you can see that in our equation we now have F s two s, three s four and FS five. These are their family side dummies. Efforts to takes a value of one If the family has to people fs two equals zero Otherwise, after three takes a value of one is the family has three people and takes a value of zero otherwise, ever as far is for family of four. And Verse five is for family with more than five people. So you don't cfs one in the equation. That is because Fs one or a family of one is the base group. We have the based group so all the coefficient of the dummies should be interpreted as the difference in that total asset compared to you the based group. So among the four Dummies, you can see that Fs two is not significant F s 32 Fs five are significant, and the level of significance of these dummies increases with the size of the families so ever sweet. It's significant at the 5% level, but s four and s wide are significant at the 1% level. Even the P value you can say that compared to the base group, a family of a single person having three or more people in the family associate with a greater average value of net total financial assets. We can also conduct a F test to see the joint significance of their family size dummies. The null hypothesis is the coefficient of the family size dummy equals each other and equals zero. We will get an F statistic with two degrees of freedom four and NYT housing 265. The statistic is 5.44 and the P value it's very, very small is way smaller than 0.1 So we are able to reject the null hypothesis. In other words, the family size dummies are jointly significant. At the 1% level, we will do a child test forward coefficient equality across five family sized categories for the test statistic we we need some of square residual from the unrestricted models and re restricted model. The restricted model comes from Part six and we use the foreign sample to estimated The sum of square residual for the respective model is 30 million. Yeah, 213,000 and 115 the for the and restricted models. They are five of them. They are estimated separately for each category of family size. The sum of square residual for and restricted models is the sum of the sum of square residual of all five models. I think them up. You wouldn't get a total of 29 million, 980,000 and 959 now, given that we have there some of square residual for the restricted model and unrestricted models, we can calculate the F statistic or the child test statistic the child has is based on the F distribution. That's why we have an F statistic. This is their formula for the F statistic. We will take the sum of square residual of the restricted model minus the sum of square of residual of the unrestricted model divided by their sum of square of residual of the unrestricted model altogether multiply with the ratio of the second degree of freedom divided by the first degree of freedom. These degrees of freedom are given from their problem. We have D F one. The first degree of freedom is the number of constraints were going to test, which is 20 and the second degrees of freedom is given as NYT housing and 245. The F statistic would be three point 57 and we can back up the P value using your statistical software. The P value for a F start with thes two degrees of freedom is very, very small. It's almost zero. So given the P value, we are able to reject the null hypotheses at the 1% level. In other words, the coefficients are not equal across family sized categories.

Part one. This is the regression result of log a wage on siblings. This is a reduced form, simple regression equation. It shows that controlling for no other factors, one more sibling in the family is associated with multi celery. That is about 2.8% lower. Let me write that down. Oh, yeah, The T statistic Armed siblings is about minus 4.7, meaning this variable is highly significant. Siblings can be correlated with many things that should have an effect on wage, including years of education. That's for sure. Hard to it's possible that older Children are given priority for higher education. Families may hit budget constraint and may not be able to afford as much education for Children born later. This is the regression result of education on birth order. This equation predicts everyone unit increase in birth order reduces predicted education by about 0.28 years. Our three when we use birth order as an instrument for education in the simple wage equation, this is what we get. This estimate is much higher than the old L s, which is point oh six and even higher than the estimate when siblings is used as an instrument for education, which is 0.1 to you too hard, for we have their reduced form equation. In order for data sub j to be identified, we need hi to you not equal zero We take the null hypothesis to be all right by two equals zero and we look to rejection of there's no hypothesis the regression of education on siblings and birth order yields Yeah, hi to hat yeah equals minus 0.153 with a standard error of point Oh 57 And that gives a T statistic of minus 2.7, which strongly rejects the null hypothesis. Mhm. This is the identification assumption appears to hold Part five. The equation estimated by instrumental variable is lage wage equals to have 4.94 plus 0.14 education plus point oh two siblings. The standard error on the estimate on education is much larger than we obtain In part three. The 95% confidence interval for beta education is roughly minus 0.1 two 0.28 which is very wide and includes the value zero. The standard error of the estimate on sibling is very large relative to the coefficient. Estimates making siblings highly insignificant. Uh huh. Yeah, yeah, yeah, right. Art six. Education had represents the first stage fitted values. The correlation between that and siblings is about minus 0.93 which is a very strong negative correlation. This means, for the purposes of using instrumental variable Monte culinary T is a serious problem. Yeah, we can still estimate the effect of education, but we would not get to estimate with much precision. Mhm, Yeah.


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