EBK BUSINESS STATISTICS
7th Edition
ISBN: 8220102743984
Author: STEPHAN
Publisher: PEARSON
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A linear relationship between EmployeeSalary (Dependent) and degree(independent) has the
following equation : Salary = 400+0.2 (Degree). SST= 736, SSR= 385. Calculate and interpret the
coefficient of determination (r2) :
Select one:
O a. 0.48 , 47.69 percent of the variability in employee salary can be explained by the simple linear
regression equation
Ob. 0.52,52.31 percent of the variability in employee salary can be explained by the simple linear
regression equation
Oc. 0.48, 47.69 percent of the variability in the degree earned can be explained by the simple linear
regression equation
F
Od. 0.52, 52.31 percent of the variability in the degree earned can be explained by the simple linear
regression equation
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A linear relationship between EmployeeSalary (Dependent) and degree(independent) has the
following equation : Salary = 400+0.2 (Degree). SST= 736, SSR= 385. Calculate and interpret the
coefficient of determination (r2) :
Select one:
O a. 0.48 , 47.69 percent of the variability in employee salary can be explained by the simple linear
regression equation
Ob. 0.52,52.31 percent of the variability in employee salary can be explained by the simple linear
regression equation
Oc. 0.48, 47.69 percent of the variability in the degree earned can be explained by the simple linear
regression equation
Od. 0.52, 52.31 percent of the variability in the degree earned can be explained by the simple linear
regression equation
F
Next page
JUN
2
12
étv
T
Ps
Lr
Consumers are often interested in the fuel efficiency of the vehicles they choose to buy, so much so that they will research the various models they consider buying. Fuel efficiency can depend on a variety of variables. In this analysis, there are 73 automobiles that are popular with consumers. A regression analysis has been performed; the dependent variable is CityMPG (EPA miles per gallon in city driving), and independent variables are Length (vehicle length in inches), Width (vehicle width in inches), Weight (vehicle weight in pounds), and ManTran (1 if manual shift transmission, 0 otherwise). The level of significance is 0.05. Use the following MegaStat output to answer questions about this regression analysis.
a. State the regression equation.
b. How would CityMPG be affected if the width of a vehicle increased by an inch?
c. Estimate the CityMPG for a vehicle with a length of 190 inches, a width of 75 inches, a weight of 4100 pounds, and a manual. Round your answer to the nearest…
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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_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardRetail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y = Retail PRICE (measured in dollars) X1 = Microprocessor SPEED (measured in megahertz) (Values in sample range from 10 to 40) x 2 = CHIP size (measured in computer processing units) (Values in sample range from 286 to 486) A first-order regression model. was fit to the data. Part of the printout follows: Parameter Estimates T FOR 0 ERROR PARAMETER = 0 PROB>ITI PARAMETER STANDARD VARIABLE DF ESTIMATE INTERCEPT 1 -373.526392 1258.1243396 -0.297 0.7676 SPEED 1 104.838940 22.36298195 4 688 0.0001 сHP 1 3.571850 3.89422935 0.917 0.3629 Identify and interpret the estimate of B2-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_forwardA 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_forwardThe St. Lucian Government is interested in predicting the number of weekly riders on the public buses using the following variables: • • • • Price of bus trips per weekThe population in the cityThe monthly income of ridersAverage rate to park your personal vehicle Determine the multiple regression equation for the data. What is the predicted value of the number of weekly riders if: price of bus trips per week = $24; population = $2,000,000; the monthly income of riders = $13,500; and average rate to park your personal vehicle = $150. Interpret the coefficient of determination.arrow_forward
- In an experiment, the independent variable is the percentage of hydrocarbons and the dependent variable is the purity of oxygen produced in a chemical distillation process that are present in the main condenser of the distillation unit. The simple linear regression and correlation analysis is performed in a sample of 9 observations. Results are as shown below: SSxx : 113.7356 SSyy = 0.5156 уу a = -4.2869 b = 0.0648 %3Darrow_forwardA researcher has developed a regression model from fourteen pairs of data points. He wants to test to determine if the slope is significantly different from zero. He uses a two-tailed test and a = 0.01. The critical tablet value is 2.718 3.012 2.650 O 3.055 O 2.168arrow_forward4b) The data shows a systolic and a diastolic blood pressure of certain patients. Find the linear regression equation, using the first variable x (systolic) as the independent variable. Find the best predicted diastolic blood pressure for a patient with a systolic blood pressure (y) reading of 140. What is the correlation coefficient, r? Using a significance level of a = 0.05, is there a significant linear relationship between systolic and diastolic blood pressure? Blood Pressure: Systolic Diastolic 112 125 115 136 143 116 123 124 elimii 70 89 65 90 97 64 SUTT nisinoo aqdM 21.SS bns aqdM 78 ahoqnis erit te zbesqz steb ils to 69 bns ago 20.EI to adimil srit terit sonabilnos 2 nistnoo aqdM 21.SS bnc agdM sgsavs arit ferli mislo a hoqnis orti roqque lovedni sonsbilnos 3028 wolsd insmsisiz tomo artezorio SeqdM 2.55 al 2.SS to sulavadi znistmoodi ezusaed mish ads toqque ton zaob 2.55 to sulsy sdt anistroo ti sausosd mislo ert hoqquz 200b to sulav orit nisinoo ton zoob 11 saussed misbb adi…arrow_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_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_forwardThe largest commercial fishing enterprise in the southeastern United States is the harvest of shrimp. In a study, researchers monitored variables thought to be related to the abundance of white shrimp. One variable the researchers thought might be related to abundance is the amount of oxygen in the water. The relationship between mean catch per tow of white shrimp and oxygen concentration was described by fitting a regression line using data from ten randomly selected offshore sites. (The "catch" per tow is the number of shrimp caught in a single outing.) Computer output is shown below. The regression equation is Mean catch per tow = -5855 + 97.4 O2 Saturation Predictor Coef SE Coef T P Constant -5855 2393 -2.45 0.040 O2 Saturation 97.4 34.62 2.81 0.023 c)Construct a 95% confidence interval for ?. (Use a table or technology. Round your answers to three decimal places.) d)What margin of error is associated with the confidence interval in part (c)? (Round your…arrow_forward
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