Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use the data in GPA 2 for this exercise.(i) Estimate the model$\quad s a t=\beta_{0}+\beta_{1} h s i z e+\beta_{2} h s i z e^{2}+u$where hsize is the size of the graduating class (in hundreds), and write the results in the justify form. Is the quadratic term statistically significant?(ii) Using the estimated equation from part (i), what is the "optimal" high school size? Justify youranswer.(iii) Is this analysis representative of the academic performance of all high school seniors? Explain.(iv) Find the estimated optimal high school size, using log(sat) as the dependent variable. Is it much different from what you obtained in part (ii)?

i) $=-3.87$ii) 19.81$/[2(2.13)] \approx 4.65$iii) Only students who actually take the SAT exam appear in the sample, so it is not representativeof all high school seniors. If the population of interest is all high school seniors, a random sampleof such students who all took the same standardized exam will be needed.iv) $n=4,137, R^{2}=.0078$

No Related Courses

Chapter 6

Multiple Regression Analysis: Further Issues

No Related Subtopics

11:55

Use the data in ATTEND for…

12:25

Use the data in TWOYEAR fo…

01:55

Based on data from a local…

05:11

Success in college College…

05:09

IQ and grades Exercise 3 (…

07:33

Use the data in MEAP9 3 to…

12:37

The data in MEAPOl are for…

01:27

For Exercises I through 25…

04:01

GPAs A college’s data abou…

09:46

Use the data in WAGEl for …

02:46

SAT Math scores In Chapter…

05:30

A well-known college uses …

05:39

The following data values …

01:50

The table shows the number…

01:43

Recall that in exercise $4…

14:03

Use the data in MLB1 for t…

01:20

Grades A college admission…

01:58

01:51

Modeling Data The table sh…

06:00

For Exercises 3 through $1…

we continue with comes or exercise them before and we're going to get the data said called G P A two for this exercise in part one, when you estimate a simple model that it's ah level level model with a quadratic term, and the dependent variable is the S A T scores An independent variable is tthe e graduating class size and hundreds h size plus the quadratic term, which is eight size squared. We just need to waste meat and stada or whatever self were using and right, uh, and present the output. Okay, so here we describe for data said, we have the combined s a T score here. Ah, eight size is indeed the size of graduating class and hundreds and wheels have the ace I squared here is already, um, transformation. Really given twice. So we're going to regress s a. T to eight size a sigh square and see what happens. Okay, bye. Correct. Number of observations. 104,000. 123237 Um, highly significant f test. However, the r squared, but it just our support here. We're just looking at our square because this one variable, it's very, very low It's less than 1% of variation in the city, scores explained by, uh, the size of graduating class. But on the other hand, the coefficients are statistically significant, all of them of the 1% level or less. And here we report the estimate equation like this estimated as though these court is 997 0.98. So this means that with zero class sized, the averages to these scores predict to be around 1000 debatable anyway, plus 19.18 size minus 2.13 8 Sites Square. Uh, what do we get from that? We get an important piece of information that the relationship between the size of graduating class and the average I see these core combine this with these court is positive but is nonlinear. And indeed, it's like a probable age, a concave function that looks like this, right? If the Y axis, we have a sixties corn. The executive, we have, ah, eight size court somewhere like that, and there's a maximum value associated with that. A size had star. Let's sit here so we have increasing but diminishing returns to class size so it gets more and more But, um, in criminal difference gets less and less and that for one point it gets down. So there is a point where the maximum of this size off them of the graduating classes but yields, Um, I don't want to say optimal, really, but it yields the maximal ah, predict the city's corporate after that number that he having two large Reggie. And Plus, this is not good for a six course, right? This makes sense now in part B, we use it the estimated equation from part one to find out what is the optimal one coat optimal because we just said it's not really optimal. It's just given this a simple regression, uh, the optimal high school size. So we want the value of a size less age size star where the predicted s a T score, Richards Maximum one here. This point here in the grab. So this is the turning point, the parabola or the inflection point, as we say in maths. And we can calculate it with a simple equation that the A size star equals to the be the one here. We don't want to buy the bite to be the three of you too. This standard thing standard formula. And we get these approximately for 1 65 Now, since the eight sizes and hundreds winning to multiply this number by 100. And we get 465 students to be that important court optimal class size. Off course. We should remember that we have a very small R squared, which shows the class size explains only a tiny time out of the variation in the city's core. So again, this should all be taken with a grain of salt or maybe many grains of salt in part three. Ah, we're being as if this analysis is representative of the academic performance of all high school seniors. Yeah, well, remember that on Lee students who actually take the S of the exam appearing to sample. So it is not really representative all high school seniors, even if it's a random sample. You know, we only have data for this which will take the city's course. So if the population of interest is all high school seniors, which it is and it should be, then we need a random sample of such students who all took the same standardized exam. OK, so It's not really representative Paul high school students. Seniors. Okay? And our four went to find the estimated optimal high school size using the log s A T as a dependent variable and receive. This is different and what we have done before. So we're gonna run the same, um, the same model, but with love, it's gonna be a lug level model. He sent a flood level. I'm just looking here. Do we have okay when it generated okay, that would generate l s a T. It was luck of us 18. Nice and easy. And we're gonna I regret this fell sad. It's not, um, is that the Senate I assessed for the flow school, but just love. Okay, we get, uh, almost the same or square slightly higher, Slightly lower rugman square error again. All our coefficients of very seriously significant. And the TV, just as you can see, our kind of similar walks it for the constant dates are extreme Teesta that we report our results right here. Right. And, uh, if we do the same calculation for eight size bar a size star story, we will get, um, year 0.1 a 0.1 96 divided by two times, 0.209 And if we do it, we get it approximately 4.6 to 9, which means that it's about 469 students now. It's the cortical, optimal place side, which is very close to what we've done with the level of a model. The deal's hot, a slightly higher number. But again, this difference is not, um is nothing to worry about is very. These numbers are very close to each other.

View More Answers From This Book

Find Another Textbook

Use the data in ATTEND for this exercise.(i) Obtain the minimum, maximum…

Use the data in TWOYEAR for this exercise.(i) The variable stotal is a s…

Based on data from a local college, a statistician determined that the avera…

Success in college Colleges use SAT scores in the admissions process because…

IQ and grades Exercise 3 (page 158$)$ included the plot shown below of schoo…

Use the data in MEAP9 3 to answer this question.(i) Estimate the model

The data in MEAPOl are for the state of Michigan in the year $2001 .$ Use th…

For Exercises I through 25, perform each of the following steps.a. State…

GPAs A college’s data about the incoming freshmen indicates that the mean of…

Use the data in WAGEl for this exercise.(i) Use OLS to estimate the equa…

SAT Math scores In Chapter $3,$ we examined data on the percent of high scho…

A well-known college uses the following formula to predict the grade average…

The following data values are from a random sample of 40 college students; t…

The table shows the numbers $N$ of college-bound seniors intending to major …

Recall that in exercise $44,$ the admissions officer for Clearwater College …

Use the data in MLB1 for this exercise.(i) Use the model estimated in eq…

Grades A college admissions officer, defending the college's use of SAT…

Modeling Data The table shows the cost of tuition and fees $M$ (in dollars) …

For Exercises 3 through $12,$ use the Wilcoxon rank sum test. Assume that th…

01:49

The labor-supply curve slopes upward ifa. leisure is a normal good.b…

Use the data in TRAFFIC2 for this exercise. Computer Exercise $\mathrm{C} 11…

14:20

Use the subset of 401 $\mathrm{KSUBS}$ with fsize$=1 ;$ this restricts the a…

12:06

The data set $\mathrm{NBASAL}$ contains salary information and career statis…

00:05

Use the data in CHARITY to answer the following questions:(i) Estimate t…

00:13

Use the data in ECONMATH to answer this question. The population model is

02:13

Compared to the social optimum, a monopoly firmchoosesa. a quantity …

02:30

A monopolistically competitive firm will increase itsproduction ifa.…

06:40

Apply the full White test for heteroskedasticity [see equation $(8.19) ]$ to…