Question

A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.

Test Scores
Student   First Test Grade   Second Test Grade
1   70   71
2   93   88
3   79   82
4   83   80
5   65   77
6   80   80
7   71   74
8   84   85
9   44   67
10   91   88
11   60   74
12   40   61
13   95   86
14   53   72
15   69   77
16   95   85
17   59   71
18   80   82
19   51   63
20   63   71
21   98   84

Step 1 of 2 :  

Using statistical software, estimate the parameters of the model

Second Test Grade=β0+β1(First Test Grade)+εi

Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

Answer 1

we will solve it by using excel and the steps are

Enter the Data into excel

Click on Data tab

Click on Data Analysis

Select Regression

Select input Y Range as Range of dependent variable as SecondTest Grade

Select Input X Range as Range of independent variable as First Test Grade.

click on labels if your selecting data with labels

click on ok.

So this is the output of Regression in Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9401
R Square	0.8837
Adjusted R Square	0.8776
Standard Error	2.7886
Observations	21.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0000	1123.2040	1123.2040	144.4406	0.0000
Residual	19.0000	147.7484	7.7762
Total	20.0000	1270.9524
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	45.7711	2.6726	17.1261	0.0000	40.1773	51.3649	40.1773	51.3649
First Test Grade	0.4313	0.0359	12.0183	0.0000	0.3562	0.5064	0.3562	0.5064

from above output we have the regression equation

estimate the parameters of the model

Second Test Grade=45.7711+0.4313(First Test Grade)+εi