Question

Shown below is a portion of an Excel output for regression analysis relating Y (dependent variable) and X (independent variable).

ANOVA
	df	SS
Regression	1	39947.80
Residual (Error)	10	8280.81
Total	11	48228.61
	Coefficients	Standard Error	t Stat	P-value
Intercept	69.190	26.934	2.569	0.02795
X	2.441	0.351	6.946	0.00004

1.   What is the estimated regression equation that relates Y to X? (2 Points)

2.   Is the regression relationship significant? Use the p-value approach and alpha = 0.05 to answer this question. (2 Points)

3.   What is the estimated value of Y if X = 37? (2 Points)

4.   Interpret the meaning of the value of the coefficient of determination which is 0.83. Be very specific. (2 Points)

Answer 1

(A) Using the given regression output data table

Regression equation can be written as

y = 69.190 + 2.441*x

(B) Yes, regression relationship is significant as we can see that the p value for the slope coefficient is 0.00004

this p value is less than significance level of 0.05, so it is significant

(C) To find the estimated value of y, put x = 37 in the regression equation

we get

= 69.190 + 2.441*37

= 69.190 + 90.317

= 159.51

(D) Given that R^2 = 0.83

or we can say 83%

this means that 83% variation in the dependent variable y can be explained by the independent variable x