do fast The average daily cost of living in dollars (x) and theaverage wage in dollars (y) in 12 regions of a country areshown in the following table.X 82 85 85 80 90 106 64 90 6990y 133133 149 132 158 159 199 137 159 150159Assume that the averages are jointly normallydistributed. Use the z-values rounded to two decimalplaces to obtain the answers.(a) Find a regression line relating the wage to the cost ofliving.Round your answer to one decimal place (e.g. 98.7).აShow Transcribed TextRound your answer to two decimal places (e.g. 98.76).Show Transcribed Textb) Test for the significance of regression using a=0.01._ hypothesis that ẞ1=0.(c) Estimate the correlation coefficient.Round your answer to three decimal places (e.g. 98.765).r=d) Test the hypothesis that p=0, using a=0.01.hypothesis that p=0.(e) Test the hypothesis that p=0.4, using a=0.05.hypothesis that p=0.4.(f) Construct a 99% confidence interval for the correlationcoefficient.Round your answers to three decimal places (e.g. 98.765).sps

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Answered: The average daily cost of living in…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section: Chapter Questions

Problem 40P: The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels....

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Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.
The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?
Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.
The file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions. a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an exponential trend to the series. Second, use Holts method with optimized smoothing constants. b. Which of these two methods appears to provide the best forecasts? Answer by comparing their MAPE values.
Management of a home appliance store wants to understand the growth pattern of the monthly sales of a new technology device over the past two years. The managers have recorded the relevant data in the file P13_05.xlsx. Have the sales of this device been growing linearly over the past 24 months? By examining the results of a linear trend line, explain why or why not.
The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.
The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next year. Comment on the performance of your model. What makes this time series more challenging to forecast?
A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?
A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of the year. The company has gathered the data given in the file P13_13.xlsx. Note that each observation corresponds to a particular truck. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
Answer in Excel: Consider the data below for the sales of widgets: 1. Using seasonal percentages or seasonal indexes, forecast the sales for each season in year 4, if the annual widgets sales is predicted to be 1500. 2. Develop a regression equation that captures both the trend and seasonality in this data. Use this equation to forecast the sales for each season in year 4. Season Year 1 Year 2 Year 3 Fall 505 240 210 Winter 555 460 365 Spring 400 310 204 Summer 560 450 394
The following time series represents the number of automobiles sold by a car dealership each of the past five months. t 1 2 3 4 5 Yt 7 12 10 13 14 (a) Construct a time series plot. What type of pattern exists in the data? The time series plot shows a linear trend.The time series plot shows a horizontal pattern. The time series plot shows a seasonal pattern.The time series plot shows a nonlinear trend. (b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. t = (c) What is the forecast for t = 6?
Use a graphing calculator to create a scatter plot and find the line of best fit and the correlation coefficient for the following data. Round to the nearest hundredth. X 5 10 15 20 25 30 35 y 1,800 1,750 1,590 1,490 1,400 1,275 1,010

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