Question

1.

Following is the R output when fitting regression model of X= miles run per week and Y= weight loss after a year.

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 64.28 8.11 7.93 0.015 *
X 1.23 0.63 1.96 0.188
-----------------
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.773 on 2 degrees of freedom
Multiple R-squared: 0.6586, Adjusted R-squared: 0.4879
F-statistic: 3.858 on 1 and 2 DF, p-value: 0.1885

Find the Slope of the regression line.

2.

Following is the R output when fitting regression model of X= miles run per week and Y= weight loss after a year.

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 64.28 8.11 7.93 0.015 *
X 1.23 0.63 1.96 0.188
-----------------
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.773 on 2 degrees of freedom
Multiple R-squared: 0.6586, Adjusted R-squared: 0.4879
F-statistic: 3.858 on 1 and 2 DF, p-value: 0.1885

Test the Hypothesis that Slope of the regression line is not zero. Use α=5%

3.

Which test we need to use in order to test hypotheses in multiple regression given below:

Model: Y= β0+ β1X1+ β2X2 +β3X3+β4X4 + ε β0+ β1X1+ β2X2 +β3X3+β4X4 + ε

Hypotheses

H0 : β1=β2=β3=β4=0H1 : βi≠0 for at least one βi  

4.

Which test we need to use in order to test hypotheses in multiple regression given below:

Model: Y= β0+ β1X1+ β2X2 +β3X3+β4X4 + ε β0+ β1X1+ β2X2 +β3X3+β4X4 + ε

Hypotheses:

H0 : β2=0H1 : β2≠0

Answer 1

Solution :

1) The slope of the regression line is

2) To test the hypothesis

. Vs.

Test Statistics

Where

t = 1.96

P value = 0.188

Fail to rejecte Ho

There is no linear relationship between X and Y

X does not contribute significantly to the model.

3) To test the hypothesis

Vs. . For at least one i..

In multiple regression analysis we used test for significance of regression coefficients.

Inshort F test is used.

The test for significance is test to determine the there is linear relationship between response Y and any of the regressor variable x1 ,x2,x3 and x4.

4)To test the hypothesis

Vs.   

In multiple regression model we used test on individual regression coefficients or t test

This test determine the linear relationship between response Y and regressor variable x2 .