{Exercise 14.23 (Algorithmic)} Given are five observations for two variables, x
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Question
{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
Explanation / Answer
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
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