EBK BUSINESS STATISTICS
7th Edition
ISBN: 9780134462783
Author: STEPHAN
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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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…
Suppose you are examining a multi-variable linear regression model that was designed to predict the weight of a person, measured in kg, using 3 predictor variables. One of the variables used in this analysis is "height", with the coefficient of this variable being equal to 3.96, with a standard error of the coefficient equal to 1.168. There are 300 datapoints in the dataset. Using this information, what would be the test statistic (t-ratio) for the test to see if the variable "height" is significant?
Only round final answer. Round to two decimal places.
Suppose a commercial developer in Vereeniging consider to purchase a group of small office buildings in an established business district. He uses multiple linear regression analysis, which was based on a sample of 35 office buildings, to estimate the value of an office building in a given area based on the following variables.
Y = Assessed value of the office building (in Rand) X1= Floor space in square meters X2= Number of offices X3= Age of the office building in years
Answer the questions that follow by typing only the letter of the correct option (A, B, C, D or E) in the answer spaces provided.
Variablesy: Valuex1: Floor Spacex2: Officesx3: Age
Model Fitting StatisticsR^2 = 0.9752Adj R^2: ?
Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates Error of Beta Estimates Error of b t Statistic Prob > |t|Intcpt…
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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_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_forward
- d) Hence test whether ? is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.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_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_forward
- Consider the SPSS regression output below. The dependent variable (Y) is the level of happiness felt by individuals. The dependent variable was measured in the following manner: 1= very unhappy, 2= somewhat unhappy, 3=neither unhappy nor happy, 4= somewhat happy, 5= very happy. The following four factors are the independent variables: highest year of school completed, respondent’s age, number of children of the respondent, and total family income. The researcher acquired data from 1,457 randomly selected Americans and ran a multiple regression. The regression results are presented below: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .215a .046 .043 .72476 a. Predictors: (Constant), TOTAL FAMILY INCOME, AGE OF RESPONDENT, NUMBER OF CHILDREN, SUBJECTIVE CLASS IDENTIFICATION, HIGHEST YEAR OF SCHOOL COMPLETED Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig.…arrow_forwardStoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 88 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−0.813+0.177?,h^=−0.813+0.177w, with standard error for the coefficient of ?w equal to 0.448. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.arrow_forwardThe regional transit authority for a major metropolitan area wants to determine whetherthere is a relationship between the age of a bus and the annual maintenance cost. A sampleof ten buses resulted in the following data: a. Develop a scatter chart for these data. What does the scatter chart indicate about therelationship between age of a bus and the annual maintenance cost?b. Use the data to develop an estimated regression equation that could be used to predictthe annual maintenance cost given the age of the bus. What is the estimated regressionmodel?c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.05level of significance. What are the correct interpretations of the estimated regressionparameters? Are these interpretations reasonable?d. How much of the variation in the sample values of annual maintenance cost does themodel you estimated in part b explain?e. What do you predict the annual maintenance cost to be for a 3.5-year-old bus?arrow_forward
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