Question

A professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter are given below.Student No. Hours Spent Studying Total Points Earned1 25 182 10 133 70 534 40 435 85 686 45 287 70 688 60 589 35 2310 55 43Simple Regression - POINTS vs. HOURSDependent variable: POINTSIndependent variable: HOURSLinear model: Y=a +b*XCoefficientsLeast Squares Standard TParameter Estimate Error Statistics P-ValueIntercept 0.437798 5.9182 0.073948 o.9428Slope 0.829539 0.109474 7.57748 0.0001Analysis of VarianceSource Sum of Squares Df Mean Square F-Ratio P-ValueModel 3249.72 1 3249.72 57.42 0.0001Residual 452.779 8 56.5974 Total (Corr.) 3702.5 9The following questions are based on the information above.1) Write down the estimated regression equation that could be used to estimate the total points earned in the course given the hours spent studying.2) At the 0.05 level of significance, does hours spent studying have a significant effect on the total points earned in this course?3) Find the standard error of the estimate.4) Use the estimated regression to predict the points of a student who spent 50 hours studying for this course.5) If a student spent 120 hours studying for this course, would you feel comfortable to use your estimated regression equation to predict his points? Why?6) What's the R-squared?7) Do you believe your estimated regression equation would provide a good prediction of the points? Use R-squared from Question 8 to support your answer.

Answer 1

Answer:

1. y = 0.437798+0.829539X

2. there is a significant effect

3. 7.523

4. 41.914

5. no

6. 0.8777

Step-by-step explanation:

1.

from the regression output we have

intercept = 0.437798

slope = 0.829539

the regression line would therefore be =

y = 0.437798 + 0.829539X

2.

h0 = regression is not significant

h1: regression is significant

alpha = 0.05

p value = 0.0001

we compare p-value with alpha

0.0001<0.05

we therefore reject H0 and conclude that hours spent studying have significant effect on total points.

3.

To get standard error of estimate:

mean sum of squared error = MSE

MSE = 56.5974

= √56.5974

= 7.523

4.

points of a student who spent 50 hours studying. we calculate this from the regression line

y = 0.437798 + 0.829539X

x = 50

y = 0.437798 + 0.829539(50)

y = 41.914

5.

no I would not be comfortable using estimate regression equation to predict his point of a student spent 120 hours studying. this value is out of range of the predictor values (independent variables)

6. to get r² (r squared)

r² = SSR/SST

SSR = 3249.72

SST = 3702.5

r² = 3249.72/3702.5

= 0.8777

7.

we are supposed to solve question 7 from question 8. but no question 8 was given. hence no solution