Question
Consider the following estimated models:Model 1: y 4,4x Model 2: y = 2 23 In(x) Model 3: 3.0 O1x; s2 0.07 In8 Model 4: 2.6 0.6 In(x); s2 0.05Interpret the slope coefficient in each of the above estimated models when x increases by one unit in Models and 3 and by 1% in Models 2 and 4. (Round your answers to 2 decimal places )Model 1: Yunits_Model 2:by aboutunits_Model 3:by about by aboutpercent.Model 4:percent:
Consider the following estimated models: Model 1: y 4,4x Model 2: y = 2 23 In(x) Model 3: 3.0 O1x; s2 0.07 In8 Model 4: 2.6 0.6 In(x); s2 0.05 Interpret the slope coefficient in each of the above estimated models when x increases by one unit in Models and 3 and by 1% in Models 2 and 4. (Round your answers to 2 decimal places ) Model 1: Y units_ Model 2: by about units_ Model 3: by about by about percent. Model 4: percent:
Answers
Use a calculator to find a regression model for the given data. Graph the scatterplot and regression model on the calculator. Use the regression model to make the indicated predictions. Find an exponential regression model for the given data:
$$\begin{array}{c|r|r|r|r|r}x & 0 & 10 & 20 & 30 & 40 \\\hline y & 350 & 570 & 929 & 1513 & 2464\end{array}$$
For this problem, we're going to do a nonlinear regression. So we have a log arrhythmic regression in this case Our ex guys are going to be 1-4 E. 12 and 16. And then our why valleys are going to be Uh to 9 11 yeah 14, 15. So changing this data here, this trend line, we want it to be log arrhythmic and as we see we'll get a fairly close log arrhythmic value. Our equation in this case is going to be if we increase its size and make a little darker, we see that it's going to be y equals 4.9364 times the natural log of X Plus 3.6407. As we see, this is fairly close to the data, we could choose perhaps better log rhythmic equation for it. But that's what the how much asking for. Um this is to 9 11, 14, 15 and there should be 124, 9, 4, 11, 8, 11. What four should go with 9? So this could be gone right here. So this should be four, there should be eight, there should be 12 and they should be 16. So we end up seeing we get a better model as a result, which is given by 4.6536 natural lagerback's plus 2.0812.
First I have to produce this get up plots and then get a regression model. I'm were used isthmus for that. This is the desk. Most of states I click on this button and then no. These extracts from negative 10 up to positive 10. And then why start from negative 10 after positive 10. But any idea? I said for the eggs, Very abu. The minimum. It's one and the maximum is 10. And then for the waiver with the minimum is three prints one and the maximum is 7.5. So, your groom, it changes today access to reflect our dear s. It's so I click here and then make sure the excesses start from negative when? After 12. And then the way I will start from negative one after 10 so that I capture on my data values. Okay, then I clicked on this plus sign. They choose table extra represents my eggs and then y will represents my why I entered of values for X. And then I entered a values for why. Okay, this is the Scud uploads I need to provide. And then for the model regression model regression equation, I type Why and I type one. And they used a total sign. I type M type X and then I tape one. They're plus B. So this value here goes in there for em. And then this value Goosen, therefore be therefore for parts in my model. Then becomes this for parts B. I have an X value, and there might find the corresponding why Value thanks. Value here is zero point fire. So all I do is I plug in 0.5 into the question and then I find a wife value. So he's in a cop leader. I have white. We call to this, and then I can a prism it This value to negative 0.3. Then for Patsy, I have a a y value. Now mice find the price one x value. So a plugging 0.54 Why? And then I find the correspondent eggs value. Do you know the letter bits off a job right here? Okay, so I have extra beat. He called to this essentially what? I'm reading his I'm dividing through by the coefficients off X. So X is it? Go to zero points. 9/8 91 and then I cannot Books meets that when
Okay for part a of this question, we're gonna be using a graft to graft this function. We can notice that it will look like us. Okay. And then use the regression model on your calculator to obtain why equals 8.9 to 35 Axe to the negative. 0.11228 to five. So this is part A, and we got this using the calculator. Okay, part be, we're gonna be using this. The model we just found to predict the value for X equals 9.2. So 8.9 to 35 times 9.2 to the negative. 0.1128 three fought to 3 8 to 5 equals approximately 6.3 onto part. See, we see that for each point, X comma y you can take the natural log to find the corresponding point. So I'm gonna make a chart over here. A little table, naturally. Axe, unnatural of Of why? Okay. 0.69 Approximately 2.1 approximately. And then we have one point 09 and 1.97 1.557 0.92 1.8 sex. You can see that we could make a scatter part of the data and we'll notice that they seem toe look like they're in a line. 34 If I were to connect these draw dotted line to show, you could see how the points look like their end a line approximately, which is what we're ending. Toe obtain. Okay, now we're onto Part D. That's a four part problem. We're using a linear regression model based on the data points that we got in part. See? And we can obtain a graph that looks something like Thus, we have four points. One, 223 four And the model. You should obtain your calculation. Be natural. Log of why equals negatives. Your 0.113121 natural of ax plus 2.9 131 This should be the linear regression model that we obtained
First you have to produce a scatter plot and then get a regression model for mates. And I'm going to use decimals to solve parts. A. This is the desk, most of sage. So I click on this button and they we note that the X value start from negative 10 to positive 10 and the white start from negative 10 to positive 10. But in Algeria, said X, the minimum value for X this one and the maximum value off X is 10. Also for why the minimum ISS one point you file and the maximum is 1.62 Good to make changes in the exist reflects out deer estates. No, in this month's I click on this and then I make changes in the excises. If you start from negative one toe positive toward and then the West start from one and then end, that's too so that through that I capture or my data values. Okay, now now I click on this plus sign and then choose Table and X Y prefers to X values and why one faced y values. So I end my values year, and then I enter the corresponding wife values notice as I entered a values for why I get a life preview of how my diagram will look like once I complete my data entry. Okay, so this is that scatter diagram we need to produce for Patsy. Now there's another part of party where we have to put use their aggression. Moto some were type. Why? And then I type one. They used it to design. And then I type am I type X I type one and then plus B. Okay, so this value here goes in for em. And then this was seen for B. Now, our regression model then becomes so I'm queens. New parties with progressive middle is why is 1/4 zul point Jewish 63697 x plus zero points 97. You were six of seven. Okay. Now for parts B, you to find a y value given an X value and the value giving is 5.7. So all we do is to plug in the X value into the question and then find a corresponding why value. Okay, so, usually a copulate, I would get the value 1.33 37 and it is suppose. Miss Lee. Quote 1.33 Okay, unless get about C. I see defending the X value given a y value. So the way value given this 1.2 fire. Now all I do is say a plug 1.25 into the question and then I find I have corresponding X value. Okay, Now, the next tape, I have 1.25 and I'm going to subtract. Is your point nice of Israel? 67 for mates. And that is equal to this. And then I conveyed it side by Houthis amount. Okay, So right by this amount and lived by this amount. And so X is 1/4 this using a cock leader, I have the value for points 3853 and it is approximately equal to 4.39