We are interested in studying the relationship between y= y score on science tes

Question

We are interested in studying the relationship between y= y score on science test and x= x score on math test using a simple regression model: y=0+1x+. Below is some of the Minitab output for the simple linear regression analysis of y on x . The sample consists of n=24

Regression Analysis

The regression equation is: science = 24.9 + 0.74 math

Predictor Coef SE Coef T P

Constant 24.9 **** 1.65 ****

math 0.74 0.370 **** ****

1. What is the point estimate for the slope 1 1 of the population regression line?

2. Find the standard error of estimate of 0 0 (i.e. SE Coef of "Constant"): 15.091

3. What is the value of the test statistic for testing the hypotheses about the slope of the population regression line, H0:1=0 H 0 1 0 versus Ha:10 H a 1 0 : 2.00

4. What is the p-value for testing H0:1=0 H 0 1 0 versus Ha:10 H a 1 0 :

5. If =0.03 0.03 , what will be your conclusion in testing H0:1=0 H 0 1 0 versus Ha:10 H a 1 0 ?

Do not reject H0:1=0 H 0 1 0

6. The 98% confidence interval of slope 1 1 is given by:

0.74 0.98

24.9 0.928

24.9 37.848

0.74 0.928

0.74 37.848

Explanation / Answer

Question 1)

Answer:

The point estimate for the slope is 0.74

Question 2)

SE = 24.9 / 1.65= 15.091

Answer:

15.091

Question 3)

t = 0.74 / 0.370 = 2

Answer:

2

Question 4)

p-value function using excel =TDIST(2,22,2)

Answer:

p-value = 0.0580

Question 5)

P-value is more than the alpha. We fail to reject the null hypothesis.

Answer:

Do not reject b1 = 0.

Question 6)

Critical t = 2.508

0.74 (-/+) ( 2.508*0.37)

Answer:

0.74 (-/+) 0.928

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