Estimate the value of r (the coefficient of correlation) for the following four

Question

Estimate the value of r (the coefficient of correlation) for the following four sets of data: The manager of a certain store wonders if there is a relationship between the weekly sales made by his twelve salespersons and their respective years of experience. He tracks each of hit salespersons' vales for a week and then creates the than at right. a. Should weekly sales or years of experience be considered the independent (explanatory) variable? Explain your answer. b. Use the graphing feature of your calculator to determine whether there appears to be a positive linear correlation, a negative linear correlation, no correlation, or a nonlinear correlation in this data. c. Later, the manager realizes he's made a mistake with some of the data, which causes him to throw out the last four pairs of numbers. After removing those points from your scatter plot, again describe the type of correlation. d. Interpret the correlation in the context of the data (i.e. as _____ increases/decreases, ...) e. Use your calculator to find the equation of the regression line for this data. (Let x represent years of experience.) f. What is the correlation coefficient, r ? (round to four decimal places) g. What is the coefficient of determination, r^2 ? (round to four decimal places) h. Interpret the coefficient of determination to describe the variation in the data. i. Use your regression line to predict the weekly sales made by a salesperson with 3.5 years of experience.

Explanation / Answer

a, here, number of years can be taken as an independent variable since the weekly sales depend on the number of years an employee has worked.

b, There appears to be a non linear correlation for the given data.

c, After removing the last four pairs, there is a positive correlation between the two.

d, As number of years increases the sales increases 0.847749 times.

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