Question

1. Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using the listed​ actress/actor ages in various​ years, find the best predicted age of the Best Actor winner that year is 44 years. Is the result within 5 years of the actual Best Actor winner, whose age was 42 years?

Best actress: 28 29 30 61 32 35 46 28 61 23 44 51

Best Actor: 44 38 37 45 52 46 58 48 40 53 52 31

1a. Find the regression of the regression line.

y=___+(__)x. (Round the constant to one decimal place as needed.)

1b. Is the result within 5 years of the actual best actor winner , whose age was 42 years?

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Best actor
Independent Variable: Best actress
Best actor = 49.637478 - 0.11036269 Best actress
Sample size: 12
R (correlation coefficient) = -0.18666218
R-sq = 0.034842768
Estimate of error standard deviation: 8.0694449

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	49.637478	7.5328008	≠ 0	10	6.5895116	<0.0001
Slope	-0.11036269	0.18368133	≠ 0	10	-0.60083786	0.5613

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	23.507254	23.507254	0.36100613	0.5613
Error	10	651.15941	65.115941
Total	11	674.66667

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
28	46.547323	3.0836224	(39.676584, 53.418062)	(27.299418, 65.795227)

Hence,

1a) Regression equation:

y = 49.6 + (-0.11)x

1b) Yes