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Use the data in MEAP9 3 to answer this question.(i) Estimate the model$$m a t h l 0=\beta_{0}+\beta_{1} \log (\text {expend})+\beta_{2} \text { lnchprg }+u$$and report the results in the usual form, including the sample size and $R$ -squared. Are the signsof the slope coefficients what you expected? Explain.(ii) What do you make of the intercept you estimated in part (i)? In particular, does it make sense toset the two explanatory variables to zero? [Hint: Recall that log $(1)=0 . ]$(iii) Now run the simple regression of $m a t h 10$ on log(expend), and compare the slope coefficient with the estimate obtained in part (i). Is the estimated spending effect now larger or smaller than in part (i)?(iv) Find the correlation between lexpend $=$ log $($expend$)$ and lnchprg. Does its sign make sense to you?(v) Use part (iv) to explain your findings in part (iii).

$-20.36+6.23 \log ($Expend$)-.30$ Lnchprg$-69.34+11.16 \log ($Expend$)$

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Chapter 3

Multiple Regression Analysis: Estimation

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Saeed A.

March 8, 2021

so does is make sense (iv)?

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Hello, everyone, Uh, this is C seven off computer excites and check the tree. So the person we wanted to use to estimate the model that max 10 TV cool to beta zero plus beta one. A lot of expenditure plus beta to lunch program. Plus you. Here. Matt Kenney is the percentage of students passing the media Matt can like Spanish is a lot of expenditure and explained that trees in it's for per student in terms of dollars and lunch program is the percentage of students in the school lunch program. So first, we estimate the model that last one is equal to constant plus bait along like expanded. A possibility, too. This is the code progress Matt Salmon Longest finishing lunch program. So the costume tomatoes you had is minus 20.36 based on one hat, which is the car coefficient on. Well, I expect she's 6.23 and made a two hand, which is the coefficient on lunch program is negative point Trio five and our squad from dis regression ease points 18 are the signs of stop coefficients what they expected. So let's see, um, Beta one had, which is a coefficient of long extended. She's positive, which means that spending more per student will increase the percentage of students passing the test. This is something would expect. Beta two hat has a negative, Uh, is the negative side. So this is the coefficient of lunch program betweens. As a percentage of students in school lunch program increases the percentage of students passing that test decreases. That's, um Well, that could be because, uh it could mean that in some schools where the percentage of students intervention program, it might be that they're spending that there could be a lot of factors, but this is a little bit weird. Maybe unexpected. Uh, OK. Second question is, what do you make with the intercept you estimated in part one in particular. Does it make sense to set it to explain it? Three variables to zero. So because your hat in the first part we find is minus 20.36 which means one large expenditure at lunch program is he called zero. Then the percentage of students passing that test is gonna be negative. 20 which, of course, doesn't make sense, because it should be in between 0 100 but ah, So let's see if that if it makes any sense explanatory variables to equal to zero. And when we actually look at the date that we see that the minimum that the large expense you get this it points something. So it doesn't make sense to set the vehicle to zero. And, uh, also in the daytime, a minimum. Uh, Thea Lunch expenditure lunch program percentages 1.4. So he could make sense to set the lunch from that vehicle to zero. That's like nobody is in the school lunch program, but from later we see that doesn't make sense to set of a stag nature to be equal to zero. Okay, okay. The question is, now run the SIM progression of maths final, just large expenditure, and we'll make lunch program and we see that now the constant is minus 69 Betas. You Matilda point beautiful on basil until days 11 point of 16. And within a compared the slope coefficient to estimate we find in the part one and we are asked to, uh is the estimated spending effecting a larger or smaller than the part one. So in part one, the crawfish most 6.23 now in part to impart tree. It is 11.16. So the effect of expenditures on students passing the math test it's bigger. 11 is bigger than 6.23. And, uh, okay, and part four is asking us to find the correlation between large expenditure and lunch program. And instead I just fruits coronation might be spending much program. It gives me coalition here, give me the coalition table. Some people expenditure and lunch programs is gonna be minus 0.19 is the coronation and the park five is asking this to use this correlation to explain the difference between these two qualifications from two different Rick rations. So in ah, regression in turn part, we have only one extra natural available large expenditure, and in part one, we have to log expended on lunch program. So when we don't include lunch program in this regression, this knocked expenditure is also gonna capture the effect of one from him on that test. There's gonna be only too available by us to lunch. For them has a negative effect. All mad at 10 and two expended Chandler for the negative correlation. Overall, we're gonna have negative negative. We're gonna have a positive by us. So which means that log, the effect of flogged expenditure on math 10 is overestimated compared to the 1st 1 So in the first part we have 6.20 to know you have 11 point of 16 which is higher, just overestimated compared to the first part. And that is because lunch program even negatively affecting that and and not explain the children's program has a negative correlation. So overall, these two negatives makes it positive, and we have a positive bias. All right. I hope that help. Thank you for watching.

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