Y=a+b1X1 +b2X2 +b3X3 Where Y = number of automobile accidents a = 7.5 bl = 3.5 b2 = 4.5 b3 = 2.5 Calculate the expected number of automobile accidents under conditions a, b, and c: X, X, (a) 2 3 (b) 3 1
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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?Under what conditions might a firm use multiple forecasting methods?
- 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 following gives the number of accidents that occurred on Florida State Highway 101 during the last 4 months: Jan Feb Mar AprMonth 1 2 3 4Number of Accidents 25 40 60 105 Using the least-squares regression method, the trend equation for forecasting is (round your responses to two decimal places): y = ? + ?xFor the E-Commerce Retail Sales (Million$) data given in the table below, provide estimates from the 1st Quarter (Q1) of 2016 to the 3rd Quarter (Q3) of 2017 by using two models: 1) Single Exponential Smoothing with α=0.3 2) Moving Average with k=2. Calculate MAPE for each model. Quarter Year Actual Q1 2016 86802 Q2 2016 92004 Q3 2016 93795 Q4 2016 124651 Q1 2017 99491 Q2 2017 106590 Q3 2017 108291 Compare two models above (Single Exponential Smoothing and Moving Average) based on their accuracies. Which forecasting method appears to be better? Using the model you choose, provide forecast for the 4th Quarter (Q4) of 2017. Assuming that this model is overestimating, find the actual value of the Q4 of 2017 based on MAPE value. Some residual graphs from the first forecast model (including wider range of E-Commerce Retail Sales data) are given below. What do these graphs tell about the model? Explain each graph.
- The following gives the number of accidents that occured on Florida State Highway 101 during the last 4 months: Month Jan Feb Mar Apr Number of accidents 25 48 60 105 Using the least-squares regression method, the trend equation for forecasting is (round your responses to two decimal places): ^ y [___] +[___] xThe following gives the number of accidents that occurred on Florida State Highway 101 during the last 4 months: Month Jan Feb Mar Apr Number of Accidents 30 48 70 90 Part 2 Using the least-squares regression LOADING... method, the trend equation for forecasting is (round your responses to two decimal places): y = enter your response here + enter your response here x Y=?+?xRestaurant Student Population Quarterly Sales 1 2 58 2 6 105 3 8 88 4 8 118 5 12 117 6 16 137 For the data above, what would be the predicted quarterly sales for a restaurant with a student population of 15 (using linear regression)?
- Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks? Week 1 2 3 4 5 Sales 150 157 162 166 177The number of internal disk drives (in million) made at a plant in Taiwan during the past 5 years follows: Year Disk Drives 1 142 2 156 3 184 4 204 5 210 a) Using simple linear regression the forecast for the number of disk drives to be made next year= 234.4 disk drives b) The mean squared error (mse) when using simple linear regression=[___] drives^2 (round your response to one decimal place)Room registrations in the Toronto Towers Plaza Hotel have been recorded for the past 9 years. To project future occupancy, management would like to determine the mathematical trend of guest registration. This estimate will help the hotel determine whether the future expansion will be needed. Given the following time-series data, develop a regression equation relating registrations to time (e.g., a trend equation). Then forecast year 11 registrations. Room registrations are in the thousands: Sr. No Year Registration (000) 1 2011 17 2 2012 16 3 2013 16 4 2014 21 5 2015 20 6 2016 20 7 2017 23 8 2018 25 9 2019 24
