Conduct a simple linear regression and answer the following questions: 1) What i

Question

Conduct a simple linear regression and answer the following questions:
1)   What is the value of the intercept of this regression equation?
2)   What is the value of the slope of this regression equation and what is its interpretation within the context of this problem?
3)   Write the equation for this logistic regression model
4)   Use the regression equation to predict the average SAT Math score for a state with 25 percent of the students taking the SAT.
5)   R2 = .700 What does this number mean?
6)   F = 25.700 Explain how F (F ratio) is calculated and what it means.
7)   Write the results in APA style.

Descriptive Statistics
   Mean   Std. Deviation   N
Percentage Taking SAT   30.69   16.815   13
Mean_Math_SAT   531.15   17.799   13

Correlations
   Percentage Taking SAT   Mean_Math_SAT
Pearson Correlation   Percentage Taking SAT   1.000   -.837
   Mean_Math_SAT   -.837   1.000
Sig. (1-tailed)   Percentage Taking SAT   .   .000
   Mean_Math_SAT   .000   .
N   Percentage Taking SAT   13   13
   Mean_Math_SAT   13   13

Variables Entered/Removeda
Model   Variables Entered   Variables Removed   Method
1   Mean_Math_SATb   .   Enter
a. Dependent Variable: Percentage Taking SAT
b. All requested variables entered.

Model Summary
Model   R   R Square   Adjusted R Square   Std. Error of the Estimate
1   .837a   .700   .673   9.615
a. Predictors: (Constant), Mean_Math_SAT

ANOVAa
Model   Sum of Squares   df   Mean Square   F   Sig.
1   Regression   2375.873   1   2375.873   25.700   .000b
   Residual   1016.897   11   92.445      
   Total   3392.769   12          
a. Dependent Variable: Percentage Taking SAT
b. Predictors: (Constant), Mean_Math_SAT

Explanation / Answer

m(Slope)=r*Sy/Sx,-0.837*17.799/16.815=-0.8859, intercept=y-mx, = 531.15-(-0.8859)*30.69=558.34

1) 558.34

2) -0.8859. This means for every increase of 1 in Percentage Taking SAT, value of Mean_Math_SAT goes down by 0.8859.

3) y=558.34-0.8859x

4) y=558.34-0.8859(25)=536.19

5) This means that 70% of the variation in the Mean_Math_SAT is accounted for by the Percentage taking SAT.

6) F=Mean Square Regression/Mean Square Residual=2375.873/92.445=25.7. The F ratio is the ratio of the mean squared regression and the mean squared residual

7)

Slope:

The slope is -0.8859 which means for every increase of 1 in Percentage Taking SAT, value of Mean_Math_SAT goes down by 0.8859.

Intercept:

The intercept is 558.34.

r^2:

0.70. This means that 70% of the variation in Mean_Math_SAT is accounted for by Percentage taking SAT.

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