The correlation between the response variable and the predictor variable could b

Question

The correlation between the response variable and the predictor variable could be best described as:

a.     Perfectly positively linear

b.     Perfectly negatively linear

c.     Positively correlated

d.     Negatively correlated

e.     No correlation exists

What is the response variable in this problem?

a.    The university

b.    Freshmen students

c.    25th Percentile ACT Score

d.    Freshmen retention rate

            e.     20 Midwest Colleges

What is the predictor variable in this problem?

a.    The university

b.    Freshmen students

c.    25th Percentile ACT Score

d.    Freshmen retention rate

e.    20 Midwest Colleges

How much variability in the Freshmen retention rate can be explained by academic performance (as measured by the 25th percentile score on the ACT)?

a.    0.4783

b.    0.0049

c.    22.9%

d.    None of the above

Is the regression model significant at 0.01 significance level?

a.    Yes

b.    No

Using the regression equation, a Midwest college has 20 as the 25th percentile ACT score. This college’s predicted Freshman retention rate is:

a.      0.478

b.      22.9%

c.      0.7864

Using the regression equation, a Midwest college has 20 as the 25th percentile ACT score. With 95% confidence, it can be concluded that this college’s true Freshman retention rate will be between

a.      0.6958 and 0.8770

b.      0.7684 and 0.8044

For every point increase in the 25th percentile ACT score, the Freshman retention rate is expected to:

a.       increase by 0.014

b.       increase by 0.7864

c.       decrease by 0.014

d.       decrease by 0.7864

e.       None of the above

Retention of students is one of the largest problems facing colleges and universitles today. Loss of students impacts revenues not only from tuition but from state and federal funding programs. If a university can understand what factors impact student retention it can form strategic plans aimed at keeping students enrolled. Academic performance is often cited as one reason that students leave. Data were collected from 20 colleges in the Midwest on the freshman retention rate (% of freshmen who stay for a second year) and the 25" percentile score on the American College Test (ACT) examination. The scatterplot and regression output are shown below Linear Equaion: FrRatRate 951+0014ACT Back to Home Page ARY OUTPUT Mukiple R R Square Standard Error 22.9% 0.0 ANOVA 9.19383 0.0049 Error Total 0.0588 00762 0.0019 95% Prediction Interval Estimate Standard Era Intercept 5.433 0.004 0.004 Enter a value for X: 20.0 Point Estimate for Y 5% Prediction ! ion Interval Est 0.8770 Lower Limit Upper Limit 0.8044

Explanation / Answer

(first part) The correlation between the response variable and the predictor variable could be best described as:

right choice is c.     Positively correlated

(second part) What is the response variable in this problem?

right choice is d.    Freshmen retention rate

(third part) What is the predictor variable in this problem?

c.    25th Percentile ACT Score

(fourth part) How much variability in the Freshmen retention rate can be explained by academic performance (as measured by the 25th percentile score on the ACT)?

c.    22.9%

(fifth part) Is the regression model significant at 0.01 significance level?

a.    Yes, since p-value=0.0049 is less than alpha=0.01

(sixth part) Using the regression equation, a Midwest college has 20 as the 25th percentile ACT score. This college’s predicted Freshman retention rate is:

c.      0.7864

(seventh part) Using the regression equation, a Midwest college has 20 as the 25th percentile ACT score. With 95% confidence, it can be concluded that this college’s true Freshman retention rate will be between

b.      0.7684 and 0.8044

(eight part) For every point increase in the 25th percentile ACT score, the Freshman retention rate is expected to:

a.       increase by 0.014

regression coefficient is 0.014

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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