Question

Below is the ANOVA table for a linear regression analysis:

Source	SS	df	MS
Lin Regression	75	1	75
Residual	1500	60	25
Total	1575	61

(a) How many people were tested?

N = ________

(b) What are the tabled (α = .05) and calculated F-values?

Ftabled = ___________

Fcalc = ___________

(c) What are the two possible values for the product moment correlation (r)?

r = _______ or _______

(d) Without calculating the interval, will the 95% confidence interval that estimates β include 0? Why or why not?

Answer 1

Solution:

Given:

Source	SS	df	MS
Lin Regression	75	1	75
Residual	1500	60	25
Total	1575	61

Part  (a) How many people were tested?

we have

df_total = N – 1

61 = N - 1

N = 61 + 1

N = 62

Part b) What are the tabled (α = .05) and calculated F-values?

df_numerator = df_regression = 1

df_denominator = df_error = 60

α = 0.05

F_tabled = 4.00

F_calc = MS_regression / MSresidual

F_calc = 75 / 25

F_calc = 3.00

Part (c) What are the two possible values for the product moment correlation (r)?

thus

thus r = -0.2182 or 0.2182

Part d) Without calculating the interval, will the 95% confidence interval that estimates β include 0? Why or why not?

Since F_calc = 3.00 < F_tabled = 4.00, regression model is insignificant. That is regression model can not be used to predict.

that also means regression slope β is insignificant or it is 0.

Thus answer is:

Yes,  the 95% confidence interval that estimates β will include 0.