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 
Pvalue 

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 pvalue 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)
(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
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