Question

Connie Harris, in charge of office supplies at First Capital Mortgage Corp., would like to predict the quantity of paper used in the office photocopying machines per month. She believes that the number of loans originated in a month influence the volume of photocopying performed. She has compiled the following recent monthly data:

Number of Loans Originated in Month Sheets of Photocopy Paper
used (1000s)
45 22
25 13
50 24
60 25
40 21
25 16
35 18
40 25
(a) Develop the least-squares estimated regression equation that relates sheets of photocopy paper used to loans originated.
(b) Use the regression equation developed in part (a) to forecast the amount of paper used in a month when 42 loan originations are expected.
(c) Compute the coefficient of determination r2. Comment on the goodness of fit.
(d) Compute the correlation coefficient.
(e) Is there a significant relationship between the two variables? Use a significance level of 0.05 and explain using numerical examples.

Answer 1

To predict the photocopy paper usage based on the number of loans originated, one must calculate the least-squares regression equation, forecast paper usage for a given number of loans, and ascertain the strength and significance of the relationship using the coefficient of determination and correlation coefficient.

Step-by-step explanation:

To answer Connie Harris’ request to predict the number of sheets of photocopy paper used (in thousands) based on the number of loans originated in a month at First Capital Mortgage Corp., we start by following these steps:

1. Decide which variable should be the independent variable and which should be the dependent variable. In this case, the number of loans originated is the independent variable, and the sheets of photocopy paper used is the dependent variable.
2. Calculate the least-squares line using the gathered data to develop the estimated regression equation in the form ý = a + bx.
3. Using the regression equation, forecast the number of sheets of photocopy paper used when 42 loans are originated.
4. Compute the coefficient of determination r² and the correlation coefficient to assess the goodness of fit and the strength of the relationship.
5. Check if there is a statistically significant relationship between the number of loans originated and sheets of photocopy paper used by referring to the p-value and comparing it to the significance level of 0.05.

Given the data and the procedure, we will now find the necessary statistics to develop the regression equation, make forecasts, and assess the relationship between the variables.

Answer 2

y = 0.325X + 7.5 ;

21.5 ;

R^2 = 0.7655 ;

r = 0.8749

Step-by-step explanation:

No. of loans originated ____ sheets of p/paper

45 ______________22

25 ______________ 13

50 _____________ 24

60 _____________ 25

40 _____________ 21

25 _____________ 16

35 _____________ 18

40 _____________ 25

Using the linear regression calculator : the linear model obtained is:

y = 0.325X + 7.5

y = predicted variable = sheets of photocopy paper

X = number of loans originated

0.325 = slope

Intercept = 7.5

B.)

X = 42

y = 0.325(42) + 7.5

y = 21.15

C.)

The Coefficient of determination as determined using the correlation coefficient calculator is :

R^2 = 0.7655 ; this means that about 76.55% of change in number of photocopy performed is explained by the number of loans originated.

D.) The correlation Coefficient (r) :

r = sqrt(R²)

r = sqrt(0.7655)

r = 0.8749

This shows that a strong positive correlation exists between the number of loans originated and the volume of photocopying done.