A manager of a car dealership believes there is a relationship between the number of salespeople on duty and the number of cars sold. Suppose the following sample is used to develop a simple regression model to predict the number of cars sold by the number of salespeople. Make the process Number of Number of Week Cars sold Salespeople 1 79 6 2 64 6 3 49 4 4 23 2 5 52 3 6 59 5 a. Find the regression line to predict the number of cars sold using the number of salespeople. b. What is the meaning of A and B coefficients? c. Estimate what the number of cars sold will be if the company has nine sellers. d. If for this problem R = .89 and R2 = .79, explain in a complete sentence what each of the values means.
Added by Peggy R.
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To do this, we can use the following formulas: B1 = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)^2 B0 = ȳ - B1 * x̄ where xi and yi are the individual data points, and x̄ and ȳ are the means of the x and y values, respectively. Using the given data, we can calculate the Show more…
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Adi S.
A manager of a car dealership believes there is a relationship between the number of salespeople on duty and the number of cars sold. Suppose the following sample is used to develop a simple regression model to predict the number of cars sold by the number of salespeople. Week: Number of cars sold: Number of sales people: 1 79 6 2 64 6 3 49 4 4 23 2 5 52 3 Answer the following questions about this problem using the following Excel report. What is the value of r2 ? Explain what r2 is telling us about the data? What is the regression equation. How many cars would you expect to be sold if there are 5 salespeople? 7 salespeople? Which of your predictions would be considered most reliable? 5 or 7 and why? Summary output: Regression statistics: r 0.908942 R Squared Adjusted R Square 0.768233 Standard Error 9.963214 Observations 5 ANOVA: df SS MS F Significance F Regression 1 1415.403 1415.403 14.25874 0.03253 Residual 3 297.7969 99.26563 Total 4 1713.2 Coefficients Standard error T Stat P-Value Lower 95% Upper 95% Intercept 9.234375 12.51613 0.737798 0.514108 -30.5975 49.06629 X Variable 1 10.51563 2.784803 3.776075 0.03253 1.653139 19.37811
Sri K.
The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car (x) is important in determining the resale value (y). He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars) as the response variable and the age of the car (in years) as the predictor variable. He found that the mean age of the used car in the sample is about 14 years and the standard deviation is about 2.6 years. The sample mean price is 17 with a standard deviation of 4. The correlation between age of cars and the prices is about -0.4. a) The slope of the regression line of yield of price on age is: b) The intercept of the regression line of yield of price on age is: c) The predicted value of the price of a used car which is 13 years old is: d) Suppose a certain used car of age 13 years is sold at a price of 2.1. The residual value of the price is: e) What percentage of the total sample variation in price is explained by the model?
Sheryl E.
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