Understanding Basic Statistics
7th Edition
ISBN: 9781305254060
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Textbook Question
Chapter 4.2, Problem 20P
Residual Plot: Miles per Gallon Consider the data of Problem 9.
(a) Make a residual plot for the least-squares model.
(b) Use the residual plot to comment about the appropriateness of the least- squares model for these data. See Problem 19.
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Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A study of external disk drives finds the data available below. The least squares line was
found to be Price = 14.00 + 66.457 Capacity with s. = 49.27 and SE (b,) = 13.2769. The assumptions and conditions for regression are met. Complete parts a through c below.
E Click the icon to view the external disk drive data.
a) Disk drives keep growing in capacity. Some tech experts now talk about the Petabyte (PB = 1000 TB = 1,000,000 GB) drives. What does this model predict that a Petabyte-capacity drive will cost?
The predicted price of a 1 PB hard drive is $
(Round to the nearest cent as needed.)
External Disk Drive Data
Capacity (TB)
0.15
0.25
0.32
Price ($)
36.00
38.95
50.50
85.00
110.00
140.00
350.00
115.78
110.27
4
Mean
1.53
SD
1.51
Print
Done
Solve the following problems completely.
An article in the Journal of Environmental Engineering (1989, Vol. 115(3), reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage).
Draw a scatter diagram of the data.
Fit the simple linear regression model using the method of least squares. Find an estimate of σ2.
Estimate the mean chloride concentration for a watershed that has 1% roadway area.
Find the fitted value corresponding to x = 0.47 and the associated residual.
Test the hypothesis H0: β1 = 0 versus H1: β1 ≠ 0 using the analysis of variance procedure with α = 0.01.
Find a 99% confidence interval of Mean chloride concentration when roadway area x = 1.0%
Find a 99% prediction interval on chloride concentration when roadway area x = 1.0%.
Plot the residuals versus ŷ and versus x. Interpret these plots.…
Solve the following statistical problems using regression analysis.
PROBLEM: Montgomery, Peck, and Vining (2001) present data concerning the performance of the 28 National Football League teams in 1976. It is suspected that the number of games won (y) is related to the number of yards gained rushing by an opponent (x). The data are shown in the following table.(a) Calculate the least squares estimates of the slope and intercept. What is the estimate of 2? Graph the regression model.(b) Find an estimate of the mean number of games won if the opponents can be limited to 1800 yards rushing.(c) What change in the expected number of games won is associated with a decrease of 100 yards rushing by an opponent?
Chapter 4 Solutions
Understanding Basic Statistics
Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Critical Thinking: Linear Correlation Look at the...Ch. 4.1 - Critical Thinking: Linear Correlation Look at the...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...
Ch. 4.1 - Interpretation Trevor conducted a study and found...Ch. 4.1 - Interpretation Do people who spend more time on...Ch. 4.1 - Veterinary Science: Shetland Ponies How much...Ch. 4.1 - Health Insurance:Administrative Cost The following...Ch. 4.1 - Meteorology: Cyclones Can a low barometer reading...Ch. 4.1 - Geology: Earthquakes Is the magnitude of an...Ch. 4.1 - Baseball: Batting Averages and Home Runs In...Ch. 4.1 - University Crime: FBI Report Do larger...Ch. 4.1 - Prob. 19PCh. 4.1 - Prob. 20PCh. 4.1 - Expand Your Knowledge: Using a Table to Test The...Ch. 4.1 - Expand Your Knowledge: Sample Size and...Ch. 4.1 - Prob. 23PCh. 4.2 - Statistical Literacy In the least-squares line...Ch. 4.2 - Statistical Literacy In the least squares line...Ch. 4.2 - Critical Thinking When we use a least-squares line...Ch. 4.2 - Critical Thinking If two variables have a negative...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Economics: Entry-Level Jobs An economist is...Ch. 4.2 - Ranching: Cattle You are the foreman of the Bar-S...Ch. 4.2 - Weight of Car: Miles per Gallon Do heavier cars...Ch. 4.2 - Basketball: Fouls Data for this problem are based...Ch. 4.2 - Auto Accidents: Age Data for this problem are...Ch. 4.2 - Auto Accidents: Age Let x be the age of a licensed...Ch. 4.2 - Incoine: Medicai Care Let x be per capita income...Ch. 4.2 - Violent Crimes: Prisons Does prison really deter...Ch. 4.2 - Education: Violent Crime The following data are...Ch. 4.2 - Research: Patents The following data are based on...Ch. 4.2 - Archaeology: Artifacts Data for this problem are...Ch. 4.2 - Cricket Chirps: Temperature Anyone who has been...Ch. 4.2 - Expand Your Knowledge: Residual Plot The...Ch. 4.2 - Residual Plot: Miles per Gallon Consider the data...Ch. 4.2 - Expand Your knowledge: Logarithmic...Ch. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4.2 - Prob. 24PCh. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4 - Statistical Literacy Suppose the scatter diagram...Ch. 4 - Critical Thinking Suppose you and a friend each...Ch. 4 - Statistical Literacy When using the least-squares...Ch. 4 - StatisticalLiteracy Suppose that for x = 3. the...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - Prob. 1UTACh. 4 - Prob. 2UTACh. 4 - Prob. 3UTACh. 4 - Prob. 4UTACh. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardQUESTION 2 Suppose that you are assigned a task to investigate the relationship between selling price and valuation of plots sold by a local municipality. Data was obtained for a random sample of ten plots. Plot Selling price ($'000) Valuation 1 120 72 2 100 68 3 140 72 4 150 70 5 155 75 6 100 50 7 150 58 8 200 90 9 80 56 10 145 70 Required: a) Use the method of least squares and estimate the regression equation between selling price and valuation & Provide an interpretation for the slope coefficient? b) Use the estimated regression equation and make a prediction for a value of the dependent variable when the independent variable is N$ 85 000. c) Calculate and interpret: (i) the coefficient of determination? (ii) Calculate and interpret the correlation coefficient?arrow_forwardStep 1: The equation of the least-squares regression line for predicting dates' heights from women's heights for the data below is predicted height of date 41.08 0.42 x woman's height Heights of women (x) 66 64 63 65 70 65 72 68 70 68 71 64 Heights of their dates (y) (Fill in the blanks below and give your answers to 2 decimal places.) The slope is m = _(1) (2) inch on average. For each additional inch of women's height, the height of the next person dated goes up by eBook Answer 1 Answer 2arrow_forward
- An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. (NEED ANSWERS FOR A, B, C, D) Please see attached for questions a. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. Do not round intermediate calculations. Compute b1 and b0 (to 1 decimal). Do not round intermediate calculations. Complete the estimated regression equation (to 1 decimal). Do not round intermediate calculations. b. What is the variable cost per unit produced (to 2 decimal)? Do not round intermediate calculations. c. Compute the coefficient of determination (to 3…arrow_forwardStep 1 of 3: Write the estimated regression equation using the least squares estimates for b0�0 and b1�1. Round to four decimal places, if necessary. Step 2 of 3: What is the mean square error for the model shown in the output? Round to four decimal places, if necessary. Step 3 of 3: What is the standard error for the model shown in the output? Round to four decimal places, if necessary.arrow_forwardDavid's Landscaping has collected data on home values (in thousands of $) and expenditures (in thousands of $) on landscaping with the hope of developing a predictive model to help marketing to potential new clients. Data for 14 households may be found in the file Landscape. Click on the datafile logo to reference the data. (NEED ANSWERS FOR C, D, and E) c. Use the least squares method to develop the estimated regression equation (to 5 decimals). d. For every additional $1000 in home value, estimate how much additional will be spent on landscaping (to 2 decimals). e. Use the equation estimated in part (c) to predict the landscaping expenditures for a home valued at $575,000 (to the nearest whole number).arrow_forward
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