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4/17/22, 12:46 AM
STA 108 Spring 2022: Homework 2
STA 108 Spring 2022: Homework 2
The assignment has to be submitted as a pdf document (or html if you are using Rmarkdown). You can write the
assignment using the tool you prefer (paper and pencil and then scan it, google doc exported as pdf, Rmarkdown,
etc) as long as the submitted file is a unique file.
The assignment has to be submitted electronically on Canvas by April 17, 2022 at 11:59 PM, submissions via
email will not be accepted. Solutions should be clear, easy to read and well organized.
The total number of points of this assignment is 35 points.
Good luck!
Problem 1 (Problem 2.1, page 89)
(4 points) A student working on a summer internship in the economic research department of a large corporation
studied the relation between sales of a product (Y , in million dollars) and population (X, in million persons) in the
firm’s 50 marketing districts. The normal error regression model was employed. The student first wished to test
whether or not a linear association between Y and X existed. The student accessed a simple linear regression
program and obtained the following information on the regression coefficients:
Parameter
Estimated.value
Confidence.limits.95.percent
Intercept
7.43
-1.18; 16.05
Slope
0.75
0.45; 1.06
The student concluded from these results that there is a linear association between Y and X. Is the conclusion
warranted? What is the implied level of significance?
Problem 2 (Problem 2.3, page 90)
(4 points) A member of a student team playing an interactive marketing game received the following computer
output when studying the relation between advertising expenditures (X) and sales (Y ) for one of the team’s
products:
Estimated regression equation: Y = 350.7 − 0.18X
Two-sided P-value for estimated slope: 0.91
The student stated: “The message I get here is that the more we spend on advertising this product, the fewer units
we sell!” Comment.
Problem 3
Consider Problem 3 of Homework 1.
1. (4 points) Calculate an approximate 95% confidence interval for each regression coefficient. Comment on
the results obtained.
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4/17/22, 12:46 AM
STA 108 Spring 2022: Homework 2
2. (4 points) Set up an hypothesis test in order to test the null hypothesis that temperature (X) has no effect on
the concentration of the air pollutant (Y ). What conclusions can you draw by looking at the confidence
intervals calculated above? What level of significance are you referring to?
3. (2 points) Calculate the R2 and comment on the result.
Problem 4
Consider Problem 4 of Homework 1.
1. (2 points) Use the lm() function to perform a simple linear regression with mpg as the response and
horsepower as the predictor. Use the summary() function to print the results. What conclusions can you
make on the relationship between horsepower and mpg? Why?
2. (2 points) Interpret the value of R2 .
3. (2 points) Can you use the results in summary() to develop a one sided test? Explain.
4. Use anova() function to print the anova table.
a. (2 points) Explain the difference between Sum Sq and mean Sq , and explain what these values represent.
b. (2 points) Explain which quantities are used in the F-value calculation. Show the steps to obtain the F-value,
starting from the quantities contained in the first three columns of the anova table.
c. (2 points) State the system of hypothesis which is being tested and comment on the p-value obtained.
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