3.7 We have 2008 data on INCOME = income per capita (in thousands of dollars) and BACHELOR percentage of the population with a bachelor's degree or more for the 50 U.S. States plus the District of Columbia, a total of N = 51 observations. The results from a simple linear regression of INCOME on BACHELOR are DIGGUR QUELOn
3.7 We have 2008 data on INCOME = income per capita (in thousands of dollars) and BACHELOR percentage of the population with a bachelor's degree or more for the 50 U.S. States plus the District of Columbia, a total of N = 51 observations. The results from a simple linear regression of INCOME on BACHELOR are DIGGUR QUELOn
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please solve 3.7 in its entirety, thanks!
![ith
th
es
is
O
r
r
batalu INCOME = 71.84. Test the null hypothesis that the elasticity is 0.85 against the alternative that it
is not 0.85, using the x = 0.05 level of significance.
of. Using Statistical Table 1, compute the approximate two-tail p-value for the t-statistic in part (e).
Using the p-value rule, do you reject the null hypothesis e = B₂ (INCOME/ENTERT) = 0.85,
versus the alternative e # 0.85, at the 10% level of significance? Explain.
3.7 We have 2008 data on INCOME = income per capita (in thousands of dollars) and BACHELOR =
percentage of the population with a bachelor's degree or more for the 50 U.S. States plus the District
of Columbia, a total of N = 51 observations. The results from a simple linear regression of INCOME
on BACHELOR are
(DAW)
INCOME = (a) +
se (2.672)
t (4.31)
nolinoubs to ha
1.029BACHELOR
(c)
(10.75)
od in
a. Using the information provided calculate the estimated intercept. Show your work.
b. Sketch the estimated relationship. Is it increasing or decreasing? Is it a positive or inverse relation-
ship? Is it increasing or decreasing at a constant rate or is it increasing or decreasing at an increasing
rate?
c. Using the information provided calculate the standard error of the slope coefficient. Show
your work.
e.
d. What is the value of the t-statistic for the null hypothesis that the intercept parameter equals 10?
The p-value for a two-tail test that the intercept parameter equals 10, from part (d), is 0.572. Show
the p-value in a sketch. On the sketch, show the rejection region if a = 0.05.
f.
Construct a 99% interval estimate of the slope. Interpret the interval estimate.
slog. Test the null hypothesis that the slope coefficient is one against the alternative that it is not one at
3DAW the 5% level of significance. State the economic result of the test, in the context of this problem.
3.8 Using 2011 data on 141 U.S. public research universities, we examine the relationship between cost per
student and full-time university enrollment. Let ACA = real academic cost per student (thousands of
dollars), and let FTESTU = full-time student enrollment (thousands of students). The least squares fit-
ted relation is ACA = 14.656 +0.266FTESTU.
a. For the regression, the 95% interval estimate for the intercept is [10.602, 18.710]. Calculate the
standard error of the estimated intercept.
b. From the regression output, the standard error for the slope coefficient is 0.081. Test the null hypoth-
esis that the true slope, B₂, is 0.25 (or less) against the alternative that the true slope is greater than
0.25 using the 10% level of significance. Show all steps of this hypothesis test, including the null
nolucion](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2F5f648975-596b-4061-87cc-12e0323f03a3%2Fcxquhqm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ith
th
es
is
O
r
r
batalu INCOME = 71.84. Test the null hypothesis that the elasticity is 0.85 against the alternative that it
is not 0.85, using the x = 0.05 level of significance.
of. Using Statistical Table 1, compute the approximate two-tail p-value for the t-statistic in part (e).
Using the p-value rule, do you reject the null hypothesis e = B₂ (INCOME/ENTERT) = 0.85,
versus the alternative e # 0.85, at the 10% level of significance? Explain.
3.7 We have 2008 data on INCOME = income per capita (in thousands of dollars) and BACHELOR =
percentage of the population with a bachelor's degree or more for the 50 U.S. States plus the District
of Columbia, a total of N = 51 observations. The results from a simple linear regression of INCOME
on BACHELOR are
(DAW)
INCOME = (a) +
se (2.672)
t (4.31)
nolinoubs to ha
1.029BACHELOR
(c)
(10.75)
od in
a. Using the information provided calculate the estimated intercept. Show your work.
b. Sketch the estimated relationship. Is it increasing or decreasing? Is it a positive or inverse relation-
ship? Is it increasing or decreasing at a constant rate or is it increasing or decreasing at an increasing
rate?
c. Using the information provided calculate the standard error of the slope coefficient. Show
your work.
e.
d. What is the value of the t-statistic for the null hypothesis that the intercept parameter equals 10?
The p-value for a two-tail test that the intercept parameter equals 10, from part (d), is 0.572. Show
the p-value in a sketch. On the sketch, show the rejection region if a = 0.05.
f.
Construct a 99% interval estimate of the slope. Interpret the interval estimate.
slog. Test the null hypothesis that the slope coefficient is one against the alternative that it is not one at
3DAW the 5% level of significance. State the economic result of the test, in the context of this problem.
3.8 Using 2011 data on 141 U.S. public research universities, we examine the relationship between cost per
student and full-time university enrollment. Let ACA = real academic cost per student (thousands of
dollars), and let FTESTU = full-time student enrollment (thousands of students). The least squares fit-
ted relation is ACA = 14.656 +0.266FTESTU.
a. For the regression, the 95% interval estimate for the intercept is [10.602, 18.710]. Calculate the
standard error of the estimated intercept.
b. From the regression output, the standard error for the slope coefficient is 0.081. Test the null hypoth-
esis that the true slope, B₂, is 0.25 (or less) against the alternative that the true slope is greater than
0.25 using the 10% level of significance. Show all steps of this hypothesis test, including the null
nolucion
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