4-22 The following data give the selling price, square footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months. Develop three regression models to pre- dict the selling price based upon each of the other factors individually. Which of these is best? SELLING PRICE ($) 84,000 79,000 91,500 120,000 127,500 132,500 145,000 164,000 155,000 168,000 172,500 174,000 175,000 177,500 184,000 195,500 195,000 SQUARE FOOTAGE 1,670 1,339 1,712 1,840 2,300 2,234 2,311 2,377 2,736 2,500 2,500 2,479 2,400 3,124 2,500 4,062 2,854 BEDROOMS 2 2 3 3 3 3 3 3 4 3 4 3 3 4 3 AGE (YEARS) 30 25 30 40 18 30 19 7 10 1 3 3 1 2 10 3
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- The Weibracht Corporation designs and manufactures custom beer steins for some of the numerous brew pubs in western North Carolina. Each stein costs Weibracht $8 to produce. The brew pubs purchase the steins from Weibracht for resale to their customers and require a 51% margin. Weibracht’s marketing director has conducted a regression analysis using historical data, resulting in the following regression line: q = -12 * p + 326, where q = slope * retail price + MWB What is the profit maximizing price that Weibracht should charge the brew pubs for these custom steins?The following data relate the sales figures of the bar in Mark Kaltenbach's small bed-and-breakfast inn in portland, to the number of guest registered that week: week guests bar sales 1 16 $330 2 12 $270 3 18 $380 4 14 $315 a) The simple linear regression equation that relates bar sales to number of guests(not to time) is (round your responses to one decimal place): Bar sales = [___]+[___]X guestsInvestigate what factors determine the number of times a person logs into Facebook per week. It is argued that these four factors are important: number of friends, age in years, whether the person is employed, and whether the student has a Twitter account. That is: FACEBOOK LOGIN=f(FRIENDS,AGE,EMPLOYED,TWITTER) Do you think other relevant explanatory variables should also be included? Name any two such variables and explain why they should be included in the regression.
- You have been presented with the following data and asked to fit statistical demand functions: PERIOD QUANTITY PRICE INCOME ADVERTISING 1 120 8.00 10 3 2 165 4.00 22 7 3 120 7.00 20 5 4 165 3.00 20 8 5 180 4.00 30 8 6 90 10.00 19 6 7 150 4.00 18 10.2 8 190 1.60 25 9.3 9 160 5.00 30 8 10 200 2.00 35 9.5 Linear Relationship Use any multiple regression packages to estimate a linear relationship between the dependent variable and the independent variables. Is the estimated demand function “good”? Why or why not? Discuss the economic implications of the various coefficients. Non-linear relationship. Select and estimate any form of non-linear relationship. Is the estimated demand function “good”? Why or why not? Compare with the linear form above. ElaborateA manufacturer is developing a facility plan to provide production capacity for its factory. The amount of capacity required in the future depends on the number of products demanded by its customers. The data below reflect past sales of its products: Year Annual Sales (number of products) Year Annual Sales (number of products) 1 490 5 461 2 487 6 475 3 492 7 472 4 478 8 458 Use simple linear regression to forecast annual demand for the products for each of the next three (3) years, by using the tabular method to: derive the values for the intercept and slope derive the linear equation plot the linear regression line develop a forecast for the firm’s annual sales for each of the next three yearsInvestigate what factors determine the number of times a person logs into Facebook per week. It is argued that these four factors are important: number of friends, age in years, whether the person is employed, and whether the student has a Twitter account. That is: FACEBOOK LOGIN=f(FRIENDS,AGE,EMPLOYED,TWITTER) Name two irrelevant explanatory variables that should not be included in the regression. Note that these two variables currently should NOT feature in the regression.
- The 2008 sales and profits of seven companies were given as follows Firm Sales ($ Billions) Profit ($ Billions) Fiat 5.7 0.27 Honda 6.7 0.12 BP 0.2 0.01 Toyota 0.6 0.04 Apple 3.8 0.05 IBM 12.5 0.46 Phillips 0.5 0.02 The estimated value for the company’s Profit can be estimated using the equation; Y ̂i = α ̂ + β ̂Xi……………………………………………………………………Eqn.1 Where; Y = Companies Profit X = Companies Sales α ̂ and β ̂ are estimated parameters in the model Calculate the sample regression line, where profit is the dependent variable (Y) and sales is the independent variable (X)SoCal Edison reported the following data for operating revenue and net income for 2001 through 2005. Year Operating Revenue (Millions), X Net Income (Millions), Y 2001 2270 96.9 2002 1482 89.1 2003 2138 103.9 2004 2260 81.6 2005 2600 78.1 Determine the least-squares regression line and interpret its slope. Estimate the net income if the operating revenue figure is $2500 million.Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…
- A finance manager employed by an automobile dealership believes that the number of cars sold in his local market can be predicted by the interest rate charged for a loan. Interest Rate (%) Number of Cars Sold (100s) 3 10 5 7 6 5 8 2 The finance manager performed a regression analysis of the number of cars sold and interest rates using the sample of data above. Shown below is a portion of the regression output. Regression Statistics Multiple R 0.998868 R2 0.997738 Coefficient Intercept 14.88462 Interest Rate -1.61538 2. Is interest rate charged for a loan the most important factor to be considered in predicting future car sales? Explain reasoning.The dealership's vice-president of marketing has requested a sales forecast at the prevailing interest rate of 7%. 3. As finance manager, what reasons would you convey to the vice-president in recommending this forecasting model? 4. Is the prediction of car sales…A finance manager employed by an automobile dealership believes that the number of cars sold in his local market can be predicted by the interest rate charged for a loan. Interest Rate (%) Number of Cars Sold (100s) 3 10 5 7 6 5 8 2 The finance manager performed a regression analysis of the number of cars sold and interest rates using the sample of data above. Shown below is a portion of the regression output. Regression Statistics Multiple R 0.998868 R2 0.997738 Coefficient Intercept 14.88462 Interest Rate -1.61538 1. Are there factors other than interest rate charged for a loan that the finance manager should consider in predicting future car sales? 2. Is interest rate charged for a loan the most important factor to be considered in predicting future car sales? Explain reasoning.The dealership's vice-president of marketing has requested a sales forecast at the prevailing interest rate of 7%. 3. As…You have been presented with the following data and asked to fit statistical demand functions:PERIOD QUANTITY PRICE INCOME ADVErtising1 120 8 10 3 2 165 4 22 7 3 120 7 20 5 4 165 3 20 8 5 180 4 30 8 6 90 10 19 6 7 150 4 18 10.2 8 190 1.6 25 9.3 9 160 5 30 8 10 200 2 35 9.5Linear Relationshipa. Use any multiple regression packages (eg. SPSS package) to estimate a linear relationship between the dependent variable and the independent variables. b. Is the estimated…