Exercise 12.23 (Algorithmic)) Given are five observations for two variables, x a

Question

Exercise 12.23 (Algorithmic)) Given are five observations for two variables, x and y. yi4 76 11 14 The estimated regression equation is = 1.2 + 2.4x. a. Compute the mean square error using the following equation (to 3 decimals) SSE b. Compute the standard error of the estimate using the following equation (to 3 decimals). SSE c. Compute the estimated standard deviation bi using the following equation (to 3 decimals). d. Use the t test to test the following hypotheses (a = .05); Compute the value of the t test statistic (to 2 decimals). The p-value is Select What is your conclusion? Select

Explanation / Answer

Result:

s2 = 2.533

s=1.592

sb1=0.503

t=4.77

p value =0.0175

Ho is rejected.

ANOVA table

Source

SS

df

MS

F

Regression

57.6

1  

57.600

22.74

Residual

7.6

3  

2.533

Total

65.2

4  

P=0.0175

Reject Ho.

Regression Analysis

r²

0.883

n

5

r

0.940

k

1

Std. Error

1.592

Dep. Var.

y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

57.6

1  

57.600

22.74

.0175

Residual

7.6

3  

2.533

Total

65.2

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

1.2000

1.6693

0.719

.5242

-4.1126

6.5126

x

2.4000

0.5033

4.768

.0175

0.7982

4.0018

ANOVA table

Source

SS

df

MS

F

Regression

57.6

1  

57.600

22.74

Residual

7.6

3  

2.533

Total

65.2

4  

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