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

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

4.   Interpret the meaning of the value of the coefficient of determination which is 0.83. Be very specific.

Answer 1

(1) Using the given output data

required regression equation is

y = 69.190 + 2.441*x

(2) Yes, slope coefficient is significant because the p value corresponding to the slope coefficient is 0.00004. This p value is less than 0.05 significance level, which means that there is a significant relationship between the independent and dependent variable

(3) Setting x = 37

we get

y= 69.190 + 2.441 * 37

= 69.190 + 90.317

= 159.51 (rounded to 2 decimals)

(4) Coefficient of determination is 0.83

converting to %, we get R^2 = 83%

so, we can say that 83% of the variation in the dependent variable can be explained by the independent variable or the regression line equation