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	3348.312
Residual	8	9529.811
Total	9	12878.123
	Coefficients	Standard Error		t Stat		P-value
Intercept	247.56	83.280	1.689		0.030
X	148.62	38.312	1.283		0.075

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



2. Is the regression relationship significant? Use a p-value and alpha = 0.05. (2 Points)



3. What is the estimated value of y if x = 3.5? (2 Points)



4. Compute the value of the coefficient of determination and interpret its meaning. Be very specific. (2 Points)

Answer 1

1:

The estimated regression equation is

y' = 247.56 + 148.62x

2:

Hypotheses are:

The p-value is 0.075

Since p-value is not less than 0.05 so we fail to reject the null hypothesis. That is there is no evidence to conclude that the regression relationship is significant.

3:

The estimated value of y for x = 3.5 is

y' = 247.56 + 148.62 * 3.5 = 767.73

4:

The coefficient of determination is

That is 26% of variation in dependent variable is explained by independent variable.