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

Answer:

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.