Question

A random sample of 20 individuals who graduated from college five years ago were asked to report the total amount of debt (in $) they had when they graduated from college and the total value of their current investments in s) resulting in the data set below. Assignment 10q1 data a) Which statement best describes the relationship between these two variables? As college debt increases current investment decreases. As college debt decreases current investment decreases. College debt is not associated with current investment. As college debt increases current investment increases. b) Develop a regression equation for predicting current investment based on college debt. What is the expected change in current investment for each additional dollar of college debt? Give your answer to four decimal places. c) When testing for a significant linear relationship in your regression analysis, what is the proper conclusion at the 0.05 level of significance? There is a significant linear relationship between college debt and current investment because the P-value is less than 0.05. We fail to reject the claim of no linear relationship between college debt and current investment because the P-value is greater than 0.05. There is a significant linear relationship between college debt and current investment because the P-value is greater than 0.05. We fail to reject the claim of no linear relationship between college debt and current investment because the P-value is less than 0.05. d) What is the predicted current investment for an individual who had a college debt of $5000? Give your answer to two decimal places. e) What proportion of the variation in current investment is explained by college debt? Give your answer to four decimal places.

Debt	Invested
23719	25664
2327	63658
23846	23405
12262	43385
18480	32649
7823	54587
10857	45145
10085	48262
14813	40983
2299	65308
18154	31977
16650	39308
16699	34346
19120	35813
10809	47704
19566	32805
8679	50647
16647	34555
17952	33647
5454	59726

Answer 1

First we need to find correlation coefficient r for the given data set , we can use excel function =CORREL (x,y) to find the value of r

A 1 Debt 2 23719 3 2327 4 23846 B Invested 25664 63658 23405 43385 32649 54587 45145 48262 40983 5 12262 6 18480 7 7823 8 10857 9 10085 10 14813 =CORREL(A2:A21,B2:B21) .-0.9889 65308 31977 11 2299 12 18154 13 16650 14 16699 39308 34346 15 19120 35813 16 10809 47704 17 19566 32805 18 8679 50647 19 16647 20 17952 34555 33647 59726 21 5454

Therefore r = -0.9889

Regression equation :

Y = b₀ + b₁ *x

Or Investment = b₀ + b₁ * Debt

b₀ is Intercept , we can find intercept using excel function =INTERCEPT( Y data set column range, x data set column range )

b₁ is Slope , we can find slope using excel function =SLOPE( Y data set column range, x data set column range )

A 1 Debt 2 23719 3 2327 4 23846 5 12262 6 18480 7 7823 8 10857 B Invested 25664 63658 23405 43385 32649 54587 45145 48262 40983 =INTERCEPT(B2:B21,A2:A267962.9978 =SLOPE(B2:B21, A2:A21) -1.8668 9 10085 10 14813 11 2299 65308 31977 39308 12 18154 13 16650 14 16699 15 19120 |34346 35813 16 10809 47704 32805 50647 17 19566 18 8679 19 16647 20 17952 21 5454 |34555 33647 59726

So we have b0 = 67962.9978 and b1 = -1.8668

Therefore regression equation :

Investment = 67962.9978 -1.8668 * Debt.

a) correlation coefficient r is negative

As college debt increases current investment decreases.

b) Investment = 67962.9978 -1.8668 * Debt.

The expected change in current investment for each additional dollar of college debt is -1.8668

c)  

H0 : There no is significant correlation exists between investment and debt.

Ha : There is significant correlation exists between investment and debt.

r = -0.9889 ,So | r | = 0.9889 , n = 20 and α = 0.05

n 0.514 15 16 17 18 19 + 20 2-tailed testing a = .1 a = .05 a = .01 0.441 0.641 0.426 0.497 0.623 0.412 0.482 0.606 0.400 0.468 0.590 0.389 0.456 0.575 0.378 0.444 0.561

Therefore critical value = 0.444

As | r | is greater than 0.444 , we reject the null hypothesis H0

There is significant linear relationship between college debt and current investement because the P value is less than 0.05

d) We are given debt = 5000

Investment = 67962.9978 - (1.8668 *5000 )

Investment = 58629

e) r = -0.9889 , so  $r^2$ = 0.9779

So 97.7923% or 0.9779