Question

Using the Instructor ranking data conduct a simple linear regression to predict a student’s scores based on the number of hours the student studies 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. R² =    What does this number mean?
5. F=     Explain how F (F ratio) is calculated and what it means.  
6. Write the results in APA style.

Class Participation	Actual grade	Hours Studying	gender
1	98	5	f
2	94	5	f
3	88	4	m
4	91	4.5	f
5	93	4.1	m
6	88	3.8	f
7	88	3	f
8	85	3	m
9	82	3	m
10	66	2	m
11	71	1	f
12	61	1	m

Answer 1

using minitab>stat>regression

we have

Regression Analysis: Score versus Hours Studying

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 1310.78 1310.78 69.18 0.000
Error 10 189.47 18.95
Total 11 1500.25

Model Summary

S R-sq R-sq(adj) R-sq(pred)
4.35277 87.37% 86.11% 80.09%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 57.89 3.35 17.27 0.000
Hours Studying 7.875 0.947 8.32 0.000 1.00

Regression Equation

Score = 57.89 + 7.875 Hours Studying

Ans 1 the value of the intercept of this regression equation is 57.89

Ans 2 ) the value of the slope of this regression equation is 7.875

interpretation : for every one hour increase in the study hours the value of grade/score in exam increase by 7.875

Ans 3 ) the regression model

Score = 57.89 + 7.875 Hours Studying

Ans 4 ) R2 = 0.8737 , it means that about 87.37 % variation in score can be explained by number of hour studying

ANs 5 ) F = 69.18 , F (F ratio) is = MS(regression) /MS(Error) = 1310.78/18.95 = 69.18

it means that model is significant tou use because F value is large than F critical value