The document presents the results of a regression analysis testing the relationship between two variables, x and y, based on 5 observations. The estimated regression equation is y = 0.2 + 2.6x. An F test was conducted to test for significance at the 0.05 level. The F ratio was calculated to be 16.35 with 1 degree of freedom for regression and 3 degrees of freedom for error. The p-value was determined to be less than 0.01, allowing the conclusion that a significant relationship exists between x and y.

1. {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 yxi12345yi3751114
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

2. 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

3. 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

4. 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?

5. 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

6. 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