Statistics Practice Problems

by | Feb 5, 2024 | Uncategorized

Description

1- Bicycling World, a magazine devoted to cycling, reviews hundreds of bicycles throughout the year. Its “Road-Race” category contains reviews of bicycles used by riders primarily interested in racing. One of the most important factors in selecting a bicycle for racing is the weight of the bicycle. The following data show the weight (pounds) and price ($) for ten racing bicycles reviewed by the magazine.

Click on the datafile logo to reference the data.

Model Weight (lb) Price ($)
Fierro 7B 17.9 2,200
HX 5000 16.2 6,350
Durbin Ultralight 15.0 8,470
Schmidt 16.0 6,300
WSilton Advanced 17.3 4,100
Bicyclette vélo 13.2 8,700
Supremo Team 16.3 6,100
XTC Racer 17.2 2,680
D’Onofrio Pro 17.7 3,500
Americana #6 14.2 8,100
(a) Choose a scatter chart below with weight as the independent variable.
(i)
(ii)
(iii)
(iv)
What does the scatter chart indicate about the relationship between the weight and price of these bicycles?
The scatter chart indicates there may be a linear relationship between weight and price.
(b) Use the data to develop an estimated regression equation that could be used to estimate the price for a bicycle given its weight. What is the estimated regression model?
Let x represent the bicycle weight.
If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x
(c) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
(i) We can conclude that neither β0 nor β1 are equal to zero, where β0 is the estimated change in price for a one pound weight increase and β1 is the estimated price for a bicycle weighing zero pounds. Neither interpretations are reasonable.
(ii) We cannot conclude that either β0 or β1 are equal to zero, where β0 is the estimated price for a bicycle weighing zero pounds and β1 is the estimated change in price for a one pound weight increase. Both interpretations are reasonable.
(iii) We can conclude that neither β0 nor β1 are equal to zero, where β0 is the estimated price for a bicycle weighing zero pounds and β1 is the estimated change in price for a one pound weight increase. The interpretation of β0 is not reasonable but the interpretation of β1 is reasonable.
(iv) We can conclude that β0 = 0 but β1 ≠ 0, where β0 is the estimated price for a bicycle weighing zero pounds and β1 is the estimated change in price for a one pound weight increase. The interpretation of β0 is not reasonable but the interpretation of β1 is reasonable.
(d) How much of the variation in the prices of the bicycles in the sample does the regression model you estimated in part (b) explain?
If required, round your answer to two decimal places.
%
(e) The manufacturers of the D’Onofrio Pro plan to introduce the 16.8 lb D’Onofrio Elite bicycle later this year. Use the regression model you estimated in part (b) to predict the price of the D’Ononfrio Elite.
If required, round your answer to the nearest whole number. Do not round intermediate calculations.
$

2- Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.


Market		 Weekly Gross Revenue
($100s)		 Television Advertising
($100s)		 Newspaper Advertising
($100s)
Mobile 101.3 5.0 1.5
Shreveport 51.9 3.0 3.0
Jackson 74.8 4.0 1.5
Birmingham 126.2 4.3 4.3
Little Rock 137.8 3.6 4.0
Biloxi 101.4 3.5 2.3
New Orleans 237.8 5.0 8.4
Baton Rouge 219.6 6.9 5.8
(a) Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable.
Let x represent the amount of television advertising.
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x
Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?
There a significant relationship between the amount spent on television advertising and weekly gross revenue. The estimated regression equation is the best estimate of the given the .
(b) How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain?
If required, round your answer to two decimal places.
%
(c) Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.
Let x1 represent the amount of television advertising.
Let x2 represent the amount of newspaper advertising.
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x1 + x2
Test whether each of the regression parameters β0, β1, and β2 is equal to zero at a 0.05 level of significance.
We conclude that β0 = 0.
We conclude that β1 = 0.
We conclude that β2 = 0.
What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
(i) β0 is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. β1 is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. β2 is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. The interpretation of β0 is not reasonable but the interpretations of β1 and β2 are reasonable.
(ii) β0 is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. β1 is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. β2 is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. The interpretation of β0 is not reasonable but the interpretations of β1 and β2 are reasonable.
(iii) β0 is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. β1 is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. β2 is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. The interpretation of β0, β1, and β2 are all reasonable.
(d) How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain?
If required, round your answer to two decimal places.
%
(e) Given the results in part (a) and part (c), what should your next step be? Explain.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(f) What are the managerial implications of these results?
Management can feel confident that increased spending on advertising results in increased weekly gross revenue. The results also suggest that advertising may be slightly more effective than advertising in generating revenue.

3- The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for the 2011 season (NFL web site, February 12, 2012).

Click on the datafile logo to reference the data.

Team Conference Yds/Att Int/Att Win%
Arizona Cardinals NFC 6.5 0.042 50.0
Atlanta Falcons NFC 7.1 0.022 62.5
Carolina Panthers NFC 7.4 0.033 37.5
Cincinnati Bengals AFC 6.2 0.026 56.3
Detroit Lions NFC 7.2 0.024 62.5
Green Bay Packers NFC 8.9 0.014 93.8
Houstan Texans AFC 7.5 0.019 62.5
Indianapolis Colts AFC 5.6 0.026 12.5
Jacksonville Jaguars AFC 4.6 0.032 31.3
Minnesota Vikings NFC 5.8 0.033 18.8
New England Patriots AFC 8.3 0.020 81.3
New Orleans Saints NFC 8.1 0.021 81.3
Oakland Raiders AFC 7.6 0.044 50.0
San Francisco 49ers NFC 6.5 0.011 81.3
Tennessee Titans AFC 6.7 0.024 56.3
Washington Redskins NFC 6.4 0.041 31.3

Let x1 represent Yds/Att.
Let x2 represent Int/Att.

(a) Develop the estimated regression equation that could be used to predict the percentage of games won, given the average number of passing yards per attempt. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
ŷ = + x1
What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit.
%
(b) Develop the estimated regression equation that could be used to predict the percentage of games won, given the number of interceptions thrown per attempt. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
ŷ = + x2
What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit.
%
(c) Develop the estimated regression equation that could be used to predict the percentage of games won, given the average number of passing yards per attempt and the number of interceptions thrown per attempt. If required, round your answer to three decimal digits. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
ŷ = + x1 + x2
What proportion of variation in the sample values of proportion of games won does this model explain? If required, round your answer to one decimal digit.
%
(d) The average number of passing yards per attempt for the Seattle Seahawks during the 2011 season was 6.8, and the team’s number of interceptions thrown per attempt was 0.028. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Seattle Seahawks during the 2011 season. (Note: For the 2011 season, the Seattle Seahawks’ record was 7 wins and 9 loses.)
If required, round your answer to one decimal digit. Do not round intermediate calculations.
%
Compare your prediction to the actual percentage of games won by the Seattle Seahawks. If required, round your answer to one decimal digit.
The Seattle Seahawks performed than what we predicted by %.
(e) Did the estimated regression equation that uses only the average number of passing yards per attempt as the independent variable to predict the percentage of games won provide a good fit?
Based on the coefficient of determination from the two models using the average number of passing yards per attempt as the independent variable, the model using only the average number of passing yards per attempt as the independent variable the best fit.

4- A sample containing years to maturity and (percent) yield for 40 corporate bonds is contained in the DATAfile named CorporateBonds (Barron’s, April 2, 2012).

Click on the datafile logo to reference the data.

(a) Choose a scatter chart below with years to maturity as the independent variable.
(i)
(ii)
(iii)
(iv)
Does a simple linear regression model appear to be appropriate?
A regression model appears to be more appropriate.
(b) Develop an estimated quadratic regression equation with years to maturity and squared values of years to maturity as the independent variables.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x + x2
How much variation in the sample values of yield is explained by this regression model?
If required, round your answer to one decimal places.
%
Test the relationship between each of the independent variables and the dependent variable at a 0.05 level of significance. How would you interpret this model?
β1 = 0 and conclude there a relationship between years to maturity and yield. β2 = 0 and conclude there a relationship between squared values of years to maturity and yield.
(c) Use Excel to create a plot of the linear and quadratic regression lines overlaid on the scatter chart of years to maturity and yield. Choose the correct chart below.
(i)
(ii)
(iii)
(iv)
Does this helps you better understand the difference in how the quadratic regression model and a simple linear regression model fit the sample data?
The graph shows difference between the fit of the linear and quadratic regression models to the data.
Which model does this chart suggest provides a superior fit to the sample data?
(d) What other independent variables could you include in your regression model to explain more variation in yield?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.

5- The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with electronic trades handled by discount brokers. As part of the survey, members were asked to rate their satisfaction with the trade price and the speed of execution, as well as provide an overall satisfaction rating. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker, summary scores were computed by computing a weighted average of the scores provided by each respondent. A portion the survey results follow (AAII website, February 7, 2012).

Brokerage Satisfaction with
Trade Price		 Satisfaction with
Speed of Execution		 Overall Satisfaction with
Electronic Trades
Scottrade, Inc. 3.2 3.1 3.2
Charles Schwab 3.3 3.1 3.2
Fidelity Brokerage Services 3.1 3.3 4.0
TD Ameritrade 2.8 3.5 3.7
E*Trade Financial 2.9 3.2 3.0
(Not listed) 2.4 3.2 2.7
Vanguard Brokerage Services 2.7 3.8 2.7
USAA Brokerage Services 2.4 3.7 3.4
Thinkorswim 2.6 2.6 2.7
Wells Fargo Investments 2.3 2.7 2.3
Interactive Brokers 3.7 3.9 4.0
Zecco.com 2.5 2.5 2.5
Firstrade Securities 3.0 3.0 3.0
Banc of America Investment Services 1.0 4.0 2.0
(a) Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker.
Let x1 represent satisfaction with Trade Price.
Let x2 represent satisfaction with speed of execution.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x1 + x2
What is the coefficient of determination?
If required, round your answers to four decimal places.
Interpret the coefficient of determination. If required, round your answer to one decimal places.
The regression model explains approximately % of the variation in the values of overall satisfaction in the sample.
(b) Use the t test to determine the significance of each independent variable. What are your conclusions at the 0.05 level of significance?
We conclude that β1 = 0. That is, there a relationship between satisfaction with trade price and overall satisfaction with the electronic trade.
We conclude that β2 = 0. That is, there a relationship between satisfaction with speed of execution and overall satisfaction with the electronic made.
(c) Interpret the estimated regression parameters. Are the relationships indicated by these estimates what you would expect?
(i) β0 is the estimated overall satisfaction with the electronic trade when satisfaction with trade price and speed of execution are both 0. β1 is the estimated change in overall satisfaction with the electronic trade if satisfaction with speed of execution is held constant and there is a 1 point increase in satisfaction with trade price. β2 is the is the estimated change in overall satisfaction with the electronic trade if satisfaction with trade price is held constant and there is a 1 poin

Order a similar assignment, and have writers from our team of experts write it for you, guaranteeing you an A

Order Solution Now