Exercise 1423 Algorithmic Given are five observations for tw

{Exercise 14.23 (Algorithmic)}
Given are five observations for two variables, x and y.

The estimated regression equation is  = 0.2 + 2.6x.

Use the F test to test the hypotheses in part (d) at a .05 level of significance.

Complete the F table below. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 3 decimals), and the F ratio (to 2 decimals).

What is the p-value?
Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 16

What is your conclusion, based on this F test?
SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists between x and y

xi	1	2	3	4	5
yi	3	7	5	11	14

Solution

Exercise 14.23 (Algorithmic)}
Given are five observations for two variables, x and y.


The estimated regression equation is  = 0.2 + 2.6x.

xi

yi

y pre

SSE

SST

SSR

x-meanx

1

3

2.8

0.04

25

27.04

4

2

7

5.4

2.56

1

6.76

1

3

5

8

9

9

0

0

4

11

10.6

0.16

9

6.76

1

5

14

13.2

0.64

36

27.04

4

Total

12.4

80

67.6

10

MEAN Y

8

Compute the mean square error using the following equation (to 3 decimals).



=12.4/3=4.133

Compute the standard error of the estimate using the following equation (to 3 decimals).



=2.033

Compute the estimated standard deviation b1 using the following equation (to 3 decimals).

=2.033/sqrt(10)=0.643

Use the t test to test the following hypotheses ( = .05):


Compute the value of the t test statistic (to 2 decimals).

t=2.6/0.643 =4.04


The p-value is
Select

less than .01

between .01 and .02

between .02 and .05

between .05 and .10

between .10 and .20

between .20 and .40

greater than .40

Item 5

What is your conclusion?
SelectConclude a significant relationship exists between x and y

Cannot conclude a significant relationship exists between x and yItem 6

Use the F test to test the hypotheses in part (d) at a .05 level of significance.

Complete the F table below. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 3 decimals), and the F ratio (to 2 decimals).

Source of Variation

Degrees of Freedom

Sum of Squares

Mean Square

F

Regression

1

67.6

67.600

16.35

Error

3

12.4

4.133

Total

4

80.0

What is the p-value?
Select

less than .01

between .01 and .025

between .025 and .05

between .05 and .10

greater than .10Item 16

What is your conclusion, based on this F test?
SelectConclude a significant relationship exists between x and y

Cannot conclude a significant relationship exists between x and y

	xi	yi	y pre	SSE	SST	SSR	x-meanx
	1	3	2.8	0.04	25	27.04	4
	2	7	5.4	2.56	1	6.76	1
	3	5	8	9	9	0	0
	4	11	10.6	0.16	9	6.76	1
	5	14	13.2	0.64	36	27.04	4
Total				12.4	80	67.6	10
	MEAN Y	8