Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 14.2, Problem 17PB
REM regression Refer to the previous exercise.
- a. Set up indicator variables for a regression model so that an F test for the regression parameters is equivalent to the ANOVA test comparing the three
means . - b. Express the null hypothesis both in terms of population means and in terms of regression parameters for the model in part a.
- c. The prediction equation from fitting the multiple regression model equals
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Chapter 14 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 14.1 - Hotel satisfaction The CEO of a company that owns...Ch. 14.1 - Prob. 2PBCh. 14.1 - Whats the best way to learn French? The following...Ch. 14.1 - Prob. 4PBCh. 14.1 - Prob. 5PBCh. 14.1 - ANOVA and box plots For two studies, each...Ch. 14.1 - Prob. 7PBCh. 14.1 - Smoking and personality A study about smoking and...Ch. 14.1 - Prob. 9PBCh. 14.1 - Prob. 10PB
Ch. 14.1 - Prob. 11PBCh. 14.2 - House prices and age For the House Selling Prices...Ch. 14.2 - Time on Facebook Do freshmen spent significantly...Ch. 14.2 - Prob. 14PBCh. 14.2 - Tukey holding time comparisons Refer to the...Ch. 14.2 - Prob. 16PBCh. 14.2 - REM regression Refer to the previous exercise. a....Ch. 14.2 - Prob. 18PBCh. 14.2 - Regression for outsourcing Refer to the previous...Ch. 14.2 - Advertising effect oil sales Each of 100...Ch. 14.3 - Reducing cholesterol An experiment randomly...Ch. 14.3 - Prob. 24PBCh. 14.3 - Political ideology in 2014 The GSS measures...Ch. 14.3 - Prob. 26PBCh. 14.3 - Corn and manure In Example 10, the coefficient of...Ch. 14.3 - Prob. 28PBCh. 14.3 - Regression for telephone holding times Refer to...Ch. 14.3 - Prob. 30PBCh. 14.3 - Income by gender and degree In 2012, the...Ch. 14.3 - Prob. 32PBCh. 14.3 - Attractiveness and getting dates The results in...Ch. 14.3 - Prob. 34PBCh. 14.3 - Regression of weight gain on diet Refer to the...Ch. 14 - Good friends and marital status Is the number of...Ch. 14 - Prob. 37CPCh. 14 - Singles watch more TV The 2014 General Social...Ch. 14 - Prob. 39CPCh. 14 - Prob. 40CPCh. 14 - Prob. 41CPCh. 14 - Prob. 42CPCh. 14 - Prob. 43CPCh. 14 - Comparing therapies for anorexia The Anorexia data...Ch. 14 - Prob. 45CPCh. 14 - Prob. 46CPCh. 14 - Prob. 47CPCh. 14 - Prob. 48CPCh. 14 - Prob. 49CPCh. 14 - Prob. 50CPCh. 14 - Prob. 51CPCh. 14 - TV watching by gender and race When we use the...Ch. 14 - Prob. 53CPCh. 14 - Prob. 54CPCh. 14 - Prob. 55CPCh. 14 - Prob. 56CPCh. 14 - Prob. 57CPCh. 14 - Prob. 59CPCh. 14 - Prob. 60CPCh. 14 - Prob. 61CPCh. 14 - Prob. 62CPCh. 14 - Prob. 63CPCh. 14 - Prob. 64CPCh. 14 - Prob. 65CPCh. 14 - Prob. 66CPCh. 14 - Prob. 67CPCh. 14 - Prob. 68CPCh. 14 - Prob. 69CPCh. 14 - Prob. 70CPCh. 14 - Prob. 71CP
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardLet’s assume a particular sample of Math classes contains several student GPAs from a minimum of 3.3 and a maximum of 4.0. The researcher would like to use a regression line to make estimations for future students who take this class and eventually graduate. Another student in a History class whose GPA is 3.1 would also like to use this regression line. (a) Can this regression line be used for the History student? Explain.arrow_forward
- A business statistics professor would like to develop a regression model to predict the final exam scores for students based on their current GPAs, the number of hours they studied for the exam, the number of times they were absent during the semester, and their genders. The data for these variables are given in the accompanying table at the bottom of this page. a) Using Excel, construct a regression model using all of the independent variables. Create the dummy variable Gen, which equals 1 for a male and 0 for a female student ( this assignment is arbitrary) complete the regression equation for the model below, where y= Score, x1= GPA, x2= Hours, x3= Absenses, and x4= Gen. y= (__) + (__)x1 + (__)x2 + (__)x3 + (__)x4 b) Test the significance of the overall regression model using a= 0.10. c) interpret the meaning of the regression coefficient for the dummy variable. d) using the p-values, identify which independent variables are significant with a= 0.10. e) construct a regression…arrow_forwardNine data points of data yield r=0.867 and the regression equation y=19.4+0.93x. Also, y=64.7. What is the best predicted value of y for x=40?arrow_forwardTAMU admissions board believes the score you get on the SAT in high school can help predict your college GPA. Below is a regression model using the SAT scores and GPA for 83 college graduates. Calculate a 70% Confidence Interval for the slope of the regression line. Use 4 decimal places.(Note: The SAT scores have been divided by 100 just to make the numbers nicer) Simple linear regression results:Dependent Variable: GPAIndependent Variable: SAT/100GPA = 1.318967 + 0.174653 [SAT/100]Sample size: 83R (correlation coefficient) = 0.1487R-sq = 0.0221Estimate of error standard deviation: 0.118302Parameter estimates: Parameter Estimate Std. Err. DF T-Stat P-Value Intercept 1.318967 0.3631 81 3.633 0.00049 Slope 0.174653 0.129086 81 1.353 0.1798 Use 4 decimal placesarrow_forward
- A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Using data collected for a sample ofn 91 houses in East Meadow, the appraiser fit the data with the following simple, linear regression model: y = 91.80 + 19.72, where x = number of rooms and y = appraised value of the house (in thousands of dollars). Additionally, the appraiser determined the coefficient of correlation to be r = .93 and the coefficient of determination to be r %3D = .86. Give a practical interpretation of the coefficient of correlation. B IUS Ix E三 三 三 E E E Insert Formula IIarrow_forwardIf I want to estimate the regression of a model by using OLS on Eveiws , and I chose the "keep it as general as possible" approach, what tests can I apply through the estimation and inference process to validate the model and the variables?arrow_forwardThe marketing manager wants to estimate the effect of the MBA program on Salary controlling for the other factors. Which regression model is the MOST appropriate? Oa. Salary = B_0+B_1 MBA + ε Ob. Salary = 3_0+ B_1 MBA + B_2 Work + e c. Salary = B_0+B_1 MBA+B_2 Work + B_3 Age +8 Od. Salary = B_0+ B_1 MBA + B_2 Work + B_3 Age +B_4 Gender + εarrow_forward
- e) Perform the F Test making sure to state the null and alternative hypothesis.arrow_forwardThe weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot. The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it is least able to make accurate predictions for the data. makes the strongest association between weight and height. minimizes the sum of the squared distances from the actual y-value to the predicted y-value. maximizes the sum of the squared distances from the actual y-value to the predicted y-value.arrow_forwardInterpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.arrow_forward
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