<Student’s name>
<Professor’s name>
a.
r=0.48603
The same we have obtained, calculating this coefficient by hand, using the formula:
Here, x,y – are variables from 1st to 200th, x-bar and y-bar are mean values.
b.
The same formula we have used for the next question, and obtain the following result.
The correlation coefficient between GPA and ACT English score is:
r=0.375592
The correlation coefficient between GPA and ACT math score is:
r=0.309685
The correlation coefficient between GPA and ACT composite score is:
r=0.444398
c.
As the highest correlation coefficient is between GPA and ACT composite score, the ACT composite score is the best predictor of cumulative GPA from all three predictors.
d.
We start our regression analysis from constructing scatter plot:
We can see, that the association is not seems to be very strong, but it is presents.
e.
As we can see, the linear regression equation is:
y=0.0731x+1.22
Or
GPA=0.0731*ACT_composite_score+1.22
f.
The coefficient of determination is very low – it is equal to 0.1975. This means, that only 19.75% of variance of GPA is explained by this model. Based on this value we can say, that the model is bad to make any forecasts or predictions.
g.
I used excel output for regression ANOVA and obtained the following:
Analysis of Variance
Source DF SS MS F P
Regression 1 10,461 10,461 48,73 0,000
Residual Error 198 42,507 0,215
Total 199 52,968
SSR=10.461
SSE=42.507
SST=52.968
Or, this could be calculated by hands, using the following formulas:
Sum of squares due to error:
SSE=
Sum of squares due to regression:
SSR=
And the total sum of squares:
SST=
It is obvious, that:
SST=SSR+SSE
