A simple linear regression model relating standardized scores on the math test with the annual family income in thousands of dollars is specified as follows:

a.Which variable (standardized test scores or family income) do you think should be the dependent variable in this regression model? Please justify your answer.[2 points]

b.What do you think are the most important variables that belong in the error term of the regression model specified above? Please justify each one of your examples. [2 points]

c.Using the data on 'math12' and 'faminc' in the Excel data file entitled 'Reading and Math' on the course webpage please estimate the regression model specified above. Descriptions of the variables in the data file are reported below.

No.

Name of variable

Description of variable

1

id

Person identifier

2

math12

Standardized score on the mathematics test

3

reading12

Standardized score on the reading test

4

faminc

Family income in thousands of dollars

5

motheduc

Mother's years of education

6

fatheduc

Father's years of education

7

female

=1 if female

8

cathhs

=1 if attended Catholic high school

9

parcath

=1 if a parent reports being Catholic

10

asian

=1 if Asian

11

black

=1 if black

12

hispanic

=1 if hispanic

13

white

=1 if white

Please report summary results containing the estimated slope and intercept with their standard errors,number of observations, Total sum of squares (SST), Regression sum of squares (SSR), and Error sum of squares (SSE).[2 points]

d.Does the sign of the slope for the relationship between the standardized scores on the math test and family income you found make intuitive sense? Please interpret and explain the slope of the simple linear regression model you estimated.[3 points]

e.At 10% level of significance, test whether family income has statistically significant effect on the standardized scores on the math test.Please clearly show all the necessary steps and explain in words what your decision about the null hypothesis means.[3 points]

f.Please calculate and interpret the coefficient of determination (R²) for the standardized scores on the math test and family income in your regression results.Does the magnitude of R² make sense to you for the linear regression model you estimated? Please explain. [2 points]

g.Calculate the correlation coefficient (r) and conduct a hypothesis test involving a null hypothesis which says there is no correlation between standardized scores on the math test and family income (r=0) against an alternative hypothesis which says there is correlation between the two variables ( r0).Conduct the test at 10% level of significance clearly showing all the necessary steps.[4 points]

h.Use the model to predict a standardized score on the math test for a student whose family earned $130,000 last year. If the student actually scored 65 points on the math test what is the resulting prediction error. Why does such a prediction error arise? Please explain.[2 points]