Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 13, Problem 67CR
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Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below.
(a) What proportion of the variation in MCAS score is explained by the explanatory variables?
(b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.
(c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.
(d) Suppose a second regression model (Model 2) was generated using only…
Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below.
(a) What proportion of the variation in MCAS score is explained by the explanatory variables?
(b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.
(c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.
(d) Suppose a second regression model (Model 2) was generated using only…
Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below.
(a) What proportion of the variation in MCAS score is explained by the explanatory variables?
(b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.
(c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.
(d) Suppose a second regression model (Model 2) was generated using only…
Chapter 13 Solutions
Introduction To Statistics And Data Analysis
Ch. 13.1 - Let x be the size of a house (in square feet) and...Ch. 13.1 - Consider the variables and population regression...Ch. 13.1 - The flow rate in a device used for air quality...Ch. 13.1 - The paper Predicting Yolk Height, Yolk Width,...Ch. 13.1 - A sample of small cars was selected, and the...Ch. 13.1 - Prob. 6ECh. 13.1 - Suppose that a simple linear regression model is...Ch. 13.1 - a. Explain the difference between the line y x...Ch. 13.1 - Prob. 9ECh. 13.1 - Hormone replacement therapy (HRT) is thought to...
Ch. 13.1 - Consider the data and estimated regression line...Ch. 13.1 - A simple linear regression model was used to...Ch. 13.1 - Consider the accompanying data on x = Advertising...Ch. 13.2 - What is the difference between and b? What is the...Ch. 13.2 - The largest commercial fishing enterprise in the...Ch. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - An experiment to study the relationship between x...Ch. 13.2 - The paper The Effects of Split Keyboard Geometry...Ch. 13.2 - The authors of the paper Decreased Brain Volume in...Ch. 13.2 - Do taller adults make more money? The authors of...Ch. 13.2 - Researchers studying pleasant touch sensations...Ch. 13.2 - Prob. 24ECh. 13.2 - Acrylamide is a chemical that is sometimes found...Ch. 13.2 - Prob. 26ECh. 13.2 - Exercise 13.18 described a regression analysis...Ch. 13.2 - Consider the accompanying data on x = Research and...Ch. 13.2 - Prob. 29ECh. 13.2 - In anthropological studies, an important...Ch. 13.3 - The graphs accompanying this exercise are based on...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The article Vital Dimensions in Volume Perception:...Ch. 13.3 - Prob. 35ECh. 13.3 - An investigation of the relationship between x =...Ch. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - In Exercise 13.19, we considered a regression of y...Ch. 13.4 - Prob. 40ECh. 13.4 - A subset of data read from a graph that appeared...Ch. 13.4 - Prob. 42ECh. 13.4 - Prob. 43ECh. 13.4 - The article first introduced in Exercise 13.34 of...Ch. 13.4 - The shelf life of packaged food depends on many...Ch. 13.4 - For the cereal data of the previous exercise, the...Ch. 13.4 - The article Performance Test Conducted for a Gas...Ch. 13.5 - Prob. 48ECh. 13.5 - Prob. 49ECh. 13.5 - A sample of n = 353 college faculty members was...Ch. 13.5 - Prob. 51ECh. 13.5 - Prob. 52ECh. 13.5 - The accompanying summary quantities for x =...Ch. 13.5 - Prob. 54ECh. 13.5 - Prob. 55ECh. 13.6 - Prob. 56ECh. 13 - Prob. 1CRECh. 13 - Prob. 2CRECh. 13 - Prob. 3CRECh. 13 - Prob. 4CRECh. 13 - Prob. 5CRECh. 13 - The accompanying graphical display is similar to...Ch. 13 - Prob. 7CRECh. 13 - Prob. 8CRECh. 13 - Consider the following data on y = Number of songs...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - Prob. 11CRECh. 13 - Prob. 12CRECh. 13 - Prob. 13CRECh. 13 - Prob. 14CRECh. 13 - The discharge of industrial wastewater into rivers...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - It is hypothesized that when homing pigeons are...Ch. 13 - Prob. 18CRECh. 13 - Prob. 57CRCh. 13 - Prob. 58CRCh. 13 - Prob. 59CRCh. 13 - The article Photocharge Effects in Dye Sensitized...Ch. 13 - Prob. 61CRCh. 13 - Prob. 62CRCh. 13 - Prob. 63CRCh. 13 - Prob. 64CRCh. 13 - Prob. 65CRCh. 13 - The article Improving Fermentation Productivity...Ch. 13 - Prob. 67CRCh. 13 - Prob. 68CRCh. 13 - Prob. 69CR
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic 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_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forward
- Suppose the athletic director at a university would like to develop a regression model to predict the point differential for games played by the men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of games, the point differential was calculated, along with the number of assists, rebounds, turnovers, and personal fouls. Use the data in the accompanying table attached below to complete parts a through e below. Assume a = 0.05. a) Using technology, construct a regression model using all three independent variables. y = __ + (_)x1 + (_)x2 + (_)x3 + (_)x4 b) Test the significance of each independent variable using a= 0.10. c) interpret the p-value for each independent variable. d) Construxt a 90% confidence interval for the regression coefficients for each independent variable and interpret the meaning. e) Using the results from…arrow_forwardThis is only one questionarrow_forwardThe general manager of an engineering firm wants to know whether a technical artist's experience influences the quality of his or her work. A random sample of 24 artists is selected and their years of work experience and quality rating (as assessed by their supervisors) recorded. Work experience (EXPER) is measured in years and quality rating (RATING) takes a value of 1 through 7, with 7 = excellent and 1 = poor. The simple regression model RATING = ẞ1 + ẞ₂EXPER+ € is proposed. The least squares estimates of the model, and the standard errors of the estimates, are RATING= 3.204 +0.076EXPER (se) (0.709) (0.044) (a) Interpret the coefficient of EXPER. (b) Construct a 95% confidence interval for B2, the slope of the relationship between quality rating and experience. In what are you 95% confident? (c) Test the null hypothesis that ẞ2 is zero against the alternative that it is not using a two-tail test and the α = 0.05 level of significance. What do you conclude? (d) Test the null…arrow_forward
- A major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter. Data were collected that show the number of new customers added during each quarter between 2015 and 2018. A multiple regression model was developed with the number of new customers as the dependent and the following four independent variables: Period (1, …, 16): A variable that measures the trend; Q1 = 1 for first quarter, Q1 = 0 otherwise; Q2 = 1 for second quarter, Q2 = 0 otherwise; Q3 = 1 for third quarter, Q3 = 0 otherwise. Questions: 1. Explain each of the four slopes (Period, Q1, Q2, Q3). 2. How many new customers would you expect in the second quarter of the following year (2019)?arrow_forwardWhat is the differed annual expenditures of two families if their annual net incomes are differed by 2000? The computed regression line has a value of a=4.32 and b=2.12.arrow_forwardA researcher interested in explaining the income levels of St. Lucian workers, developed the following multiple linear regression model: INC = a + BEDU + YEXP+ ST RN where INC = monthly income, EDU = the number of years of formal education, EXP = the number of years of workforce experience and TRN = the number of weeks spent in job training. A sample of 35 workers was processed using MINITAB and the following is an extract of the output obtained: %3D PredictorCoef StDev t-ratio Constant 3315.7 1371.6 2.41 EDU 116.53 26.07 4.47 EXP 282.96 222.8 1.27 TRN -318.12125.74-2.53 S= 2.05 R-sq = 77.3% R-sq(adj) = 75.2% The coefficient y is significant at the 5% level of significance. Select one: O True Falsearrow_forward
- D& T LTD marketing team needed more information about the effectiveness of their 3 main mode of advertising. To determine which type is the most effective, the manager collected one week’s data from 25 randomly selected stores. For each store, the following variables were recorded: Weekly gross sales Weekly expenditure on direct mailing (Direct) Weekly expenditure on newspaper advertising (Newspaper) Weekly expenditure on television commercials (Television) Following is the regression output based on the above-mentioned data. SUMMARY OUTPUT Regression Statistics Multiple R 0.442…arrow_forwardUsing data from the 2008 General Social Survey (GSS), political psychologists were interested in whether speaking a language other than English (1=yes, 2=no) and political views (1=extremely liberal, 7=extremely conservative) would predict attitudes toward the number of immigrants there should be in the United States (1=should be increased a lot, 5=should be reduced a lot). Write out the regression model and explain what the bs and a mean. Which predictor variable contributed more to the model? Show evidence.arrow_forwardSuppose the following data were collected from a sample of 15 houses relating selling price to square footage and the architectural style of the house. Use statistical software to find the following regression equation: PRICEi=b0+b1SQFTi+b2COLONIALi+b3RANCHi+ei . Is there enough evidence to support the claim that on average, houses that are ranch style have lower selling prices than houses that are Victorian style at the 0.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."Selling Price Square Footage Colonial (1 if house is Colonial style, 0 otherwise) Ranch (1 if house is Ranch style, 0 otherwise) Victorian (1 if house is Victorian style, 0 otherwise) 377640 1941 1 0 0 460996 3397 0 1 0 405781 2764 0 0 1 407216 2906 0 0 1 435139 3401 1 0 0 405275 2600 0 0 1 381141 2203 0 1 0 370490 2046 1 0 0 404070 2210 0 0 1 460196 3692 0 1 0 382780 2172 1 0 0 406466 2606 0 1…arrow_forward
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