Practice 1: Simple Regression Practice 2: Multiple Regression nvest Profit Time Invest Profit 5 1 5 7 13 2 7 13 8 16 3 16 12 25 4 12 25 10 19 10 19 15 32 6 15 32 16 7 16
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- 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?The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?In multiple regression analysis, testing the significance of individual regression coefficients is based on A t statistic A z statistic An F statistic
- Discuss how the advantages of using simple regression could benefit the organization.1.) Use the following dummy variables to develop an estimated regression equation to account for seasonal effects only in the data. Qtr1 = 1 if Quarter 1, 0otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise, Qtr3 = 1 if Quarter 3, 0otherwise. Based only on the seasonal effects in the data, compute estimates of quarterly sales for year 6.a. Report the estimate of sales for Year 6 Quarter 1. (Enter a whole value.)b. Report the estimate of sales for Year 6 Quarter 4. (Enter a whole value.)2.) Let Period t = 1 refer to the observation in quarter 1 of year 1; Period t = 2refer to the observation in quarter 2 or year 1; … and Period t = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and Period (t), develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the estimates of quarterly sales for year 6.a. Report the estimate…Describe the Nonlinear and Multiple Regression Analysis?
- What is Multiple regression analysis?What is the difference between linear and multiple regression?Curry Rubber manufactures rubber bands for retail companies. The accounting manager has performed a regression analysis of past data. You notice that the formula has an R-squared of .6, at-value of 2.3, and a standard error of the estimate of $200,000. The estimate for next quarter costsis $2,584,072. What do these statistics tell you about the reliability and precision of his regressionanalysis?
- Cross-Sectional Regression Analysis WasteTec is a large construction company that specializesin the construction of large wastewater treatment plants and recycling plants. A major cost driver ineither type of facility is the capacity of the plant. For example, the capacity of a recycling plant ismeasured by the number of tons of water per day (TPD) that the plant can process. These plants canvary in size from a few hundred TPD to as many as several thousand TPD. Regression analysis is auseful method to estimate the cost of a new plant by using a regression equation developed from priorplant construction projects. The dependent variable of the regression is the actual construction costsof each project, while the independent variable is the TPD for the plant. Below is a sample of somerecent projects and the related construction costs (in thousands):TPD CostsCommerce, CA 360 $ 59,369Hudson Falls, NY 400 77,013Layton, UT 420 50,405Oxford Township, NJ 450 75,779Savannah, GA 500…Explain three (3) of the general assumptions of a Regression (Least Squares) model.Write Comments on the Use of Linear Regression Analysis?