The scatterplot and the regression output below are for numbers of students enro

Question

The scatterplot and the regression output below are for numbers of students enrolled in a variety of courses in a region’s colleges and universities, and the percentages of students in those courses receiving F or W grades.

i. What is the correlation r?

ii. What does the data suggest is the relationship between class size and grade?

iii. If the failure rate is the explanatory variable and enrolment is the response, what would happen to the regression line and why?

iv. Use the regression line to predict the failure rate for a business statistics course with an enrolment of 300 students.

v. If in fact the business statitics course with an enrolment of 300 students had a failure of 46 percent, find the residual (prediction error) for your prediction in part (iv). (

vi. Comment on if this model can be used to make predictions.

The regression equation is %Forw 40.8-0.0231 Enrollment Predictor Constant Enrollme S = 8.383 Coef 40.801 0.02307 SE Coef 3.541 0.01043 11.52 0.000 2.21 0.045 R-Sq = 27.4% R-Sq(adj) 21.8% = 50 40 30 20 00 200 300 400 500 600 700 800 900 Enrollment

Explanation / Answer

i. What is the correlation r?

Correlation r = sqrt(R2) = sqrt(0.274) = -0.5235 [ as slope coefficent is negative here]

ii. What does the data suggest is the relationship between class size and grade?

Data suggests a negative weak moderate linear relationship between class size and grade.

iii. If the failure rate is the explanatory variable and enrolment is the response, what would happen to the regression line and why?

if this two variables positions will be reversed. Value of r will be the same. But slope coeficient will be changed to (1/B1) = (-1/0.02307) = -43.346 and The regression line would be a downward slope.

iv. Use the regression line to predict the failure rate for a business statistics course with an enrolment of 300 students.

Failure rate (enrolment = 300) = 40.8 - 0.02307 * 300 = 33.88 %

v. If in fact the business statitics course with an enrolment of 300 students had a failure of 46 percent, find the residual (prediction error) for your prediction in part (iv).

Residual = 46% - 33.88% = 12.12%

vi. Comment on if this model can be used to make predictions.

No, this model is not much effective as thr r value is very moderate. Even we can say that slope coefficient is significant in nature but only 27% of variability can be explained by enrollment level.

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