The chart below lists the sales in thousands of dollars based on the advertising budget for that quarter. The regression equation is Y' = 4.073 + 0.8351X. What is the correlation coefficient? Advertising ($hundreds) Sales ($thousands) 0 5 3 5.5 4 7 5 7.8 6 9 7 11 Multiple Choice 0.775 0.844 0.926 1.00
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Given values: x = 0, 3, 4, 5, 6, 7 y = 5, 5.5, 7, 7.8, 9, 11 Mean of x (x̄) = (0 + 3 + 4 + 5 + 6 + 7) / 6 = 25 / 6 = 4.1667 Mean of y (ȳ) = (5 + 5.5 + 7 + 7.8 + 9 + 11) / 6 = 45.3 / 6 = 7.55 Show more…
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Exercise 3: The following data shows the amounts of advertising budgets and annual sales for a given company. Ads: 45 52 46 48 50 47 53 49 51 Sales: 9.5 11 9.7 9.8 10 9.7 11 9.9 10 a) Calculate the Pearson's correlation coefficient between sales and advertising expenditure. b) Compute the parameter estimates (𝛽0 and 𝛽1) for the linear regression model Sales = 𝛽0 + 𝛽1Advertising + 𝜀. c) Using the model in b), compute the predicted sales for an advertising expenditure of $44,000.
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The table shows the advertising expenditures $x$ and sales volumes $y$ for a company for seven randomly selected months. Both are measured in thousands of dollars. (a) Use the regression feature of a graphing utility to find a linear model for the data. (b) Use the graphing utility to plot the data and graph the model in the same viewing window. (c) Interpret the slope of the model in the context of the problem. (d) Use the model to estimate sales for advertising expenditures of $\$ 1500$.
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