A random sample of 20 individuals who graduated from college five years ago were

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 $) resulting in the data set below.

Assignment 10q1 data

a) Which statement best describes the relationship between these two variables?

As college debt decreases current investment decreases.

As college debt increases current investment increases.

As college debt increases current investment decreases.

College debt is not associated with current investment.

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?

A. There is a significant linear relationship between college debt and current investment because the P-value is greater than 0.05.

B. 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.

C. 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.

D. There is a significant 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.  

Data: https://www.webassign.net/userimages/10q1r1.csv?db=v4net&id=287912

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 A random sample of 20 Individuals who graduated from college flve years ago were asked to report the total amount of debt (In $) they had when they graduated from college and the total value of thelr current investments (in $) resulting in the data set below. Assignment 10q1 data a) Which statement best describes the relationship between these two variables? As college debt decreases current Investment decreases. As college debt increases current investment Increases. As college debt increases current investment decreases. College debt is not associated with current investment. b) Develop a regression equation for predicting current investment based on college debl. What is the expected change in current investment for each additional dollar of college debl? Give your answer to four decimal places. C) When testing for a significant linear relatonship in your regression analysis, what is the proper conclusion at the 0.05 level of significance? There is a significant linear relationship betwe 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 we fall to relect 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 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 hy college debt? Give your answer to four decimal places.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Invested
Independent Variable: Debt
Invested = 67962.998 - 1.8667973 Debt
Sample size: 20
R (correlation coefficient) = -0.98885578
R-sq = 0.97783575
Estimate of error standard deviation: 1842.8719

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

b) Expected change = 1.8668

c) There is significant linear relationship between college debt and current investment because p - value is less than 0.05.

Option D is correct.

d) Predicted current investment = 58629.01

e) Proportion of variation explained = 0.9778

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 67962.998 1003.4945 0 18 67.726326 <0.0001 Slope -1.8667973 0.066245214 0 18 -28.180108 <0.0001

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.