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. 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 Charles H.
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Step 1:** Calculate the beta coefficient using the formula: \[ \beta = \frac{\sum (y_i - \bar{y})(x_i - \bar{x})}{\sum (x_i - \bar{x})^2} \] ** Show moreā¦
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A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on the employee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. Complete parts a through d. df SS Regression 1 94.877734 Residual 23 248.042266 Total 24 342.92 Coefficients Standard Error Intercept 7.050834 1.191639 Slope 0.660557 0.222703 a. Predict the sales next month for an employee with 3.5 years of experience. b. Compute the coefficient of determination and its meaning. c. Do the sample data provide evidence that the model is useful for predicting average monthly sales for employees based on their sales experience using a = .05? d. Construct a 95% confidence interval around the sample slope and interpret its meaning.
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