a. Does the academic performance depend on the enrollment? Do you expect a positive or a negative relationship between these two variables? b. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part a. c. Interpret the meaning of the values of and b, calculated in part b.

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The following output from R presents the results from computing a linear model.
In our data example we are interested to study the relationship between students' academic performance
api00 with variable enroll which is the number of students in the school.
Call:
1m (formula = api00 ~ enroll, data = d)
Residuals:
Min
10
Median
30
Маx
-285.50 -112.55
-6.70
95.06
389.15
Coefficients:
Estimate Std. Error t value Pr(>|t|)
< 2e-16 ***
(Intercept) 744.25141
15.93308
46.711
enroll
-0.19987
0.02985
-6.695 7.34e-11 ***
---
Signif. codes:
O '***' 0.001 '**' 0.01 '*' 0.05 '.'
0.1
1
Residual standard error: 135 on 398 degrees of freedom
Multiple R-squared:
F-statistic: 44.83 on 1 and 398 DF,
0.1012, Adjusted R-squared:
0.09898
p-value: 7.339e-11
Transcribed Image Text:The following output from R presents the results from computing a linear model. In our data example we are interested to study the relationship between students' academic performance api00 with variable enroll which is the number of students in the school. Call: 1m (formula = api00 ~ enroll, data = d) Residuals: Min 10 Median 30 Маx -285.50 -112.55 -6.70 95.06 389.15 Coefficients: Estimate Std. Error t value Pr(>|t|) < 2e-16 *** (Intercept) 744.25141 15.93308 46.711 enroll -0.19987 0.02985 -6.695 7.34e-11 *** --- Signif. codes: O '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 1 Residual standard error: 135 on 398 degrees of freedom Multiple R-squared: F-statistic: 44.83 on 1 and 398 DF, 0.1012, Adjusted R-squared: 0.09898 p-value: 7.339e-11
a. Does the academic performance depend on the enrollment? Do you expect a positive or a negative
relationship between these two variables?
b. Find the least squares regression line by choosing appropriate dependent and independent variables
based on your answer in part a.
c. Interpret the meaning of the values of b, and bị calculated in part b.
d. Predict the monthly auto insurance premium for a driver with 10 years of driving experience.
e. Compute the standard deviation of errors.
f-Construct a 90% confidence interval for slope f
g. Using alpha=D0.05, test whether B, is different from zero
h. Test at a 5% significance level whether B, is negative.
i. Following is the scatter diagram and the regression line.
008 o
o 00
00
00, o
O 00
o o00
200
400
600
800
1000
1200
1400
1600
enroll
j. Which point is an outlier?
k. Is the outlier influential? Explain.
Transcribed Image Text:a. Does the academic performance depend on the enrollment? Do you expect a positive or a negative relationship between these two variables? b. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part a. c. Interpret the meaning of the values of b, and bị calculated in part b. d. Predict the monthly auto insurance premium for a driver with 10 years of driving experience. e. Compute the standard deviation of errors. f-Construct a 90% confidence interval for slope f g. Using alpha=D0.05, test whether B, is different from zero h. Test at a 5% significance level whether B, is negative. i. Following is the scatter diagram and the regression line. 008 o o 00 00 00, o O 00 o o00 200 400 600 800 1000 1200 1400 1600 enroll j. Which point is an outlier? k. Is the outlier influential? Explain.
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