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)

Show all steps please

Answer 1

Solution:

Given:

ANOVA
	df	SS
Regression	1	39947.8
Residual (Error)	10	8280.81
Total	11	48228.61
	Coefficients	Standard Error	t Stat	P-value
Intercept	69.19	26.934	2.569	0.02795
X	2.441	0.351	6.946	0.00004

Part 1. What is the estimated regression equation that relates Y to X?

Y = a + b* X

Y = 69.19 + 2.441 * X

Part 2.  Is the regression relationship significant?

H0: the regression relationship is NOT significant

Vs

H1: the regression relationship is significant

P-value = 0.00004

Decision Rule: Reject H0, if P-value < 0.05 level of significance, otherwise we fail to reject H0

Since P-value = 0.00004 < 0.05 level of significance, we reject H0.

Thus we conclude that: the regression relationship is significant

Part 3.  What is the estimated value of Y if X = 37?

Y = 69.19 + 2.441 * X

Y = 69.19 + 2.441 * 37

Y = 69.19 + 90.317

= 159.507

Part 4. Interpret the meaning of the value of the coefficient of determination which is 0.83.

The coefficient of determination = r² = 0.83 = 83%

About 83% of the variation in dependent variable Y is explained by linear regression model.