Suppose data on advertising expenditures and revenue (both in thousands of dollars) for a certain restaurant follow. Advertising Expenditures Revenue 1 18 2 32 4 44 6 41 10 51 14 53 20 55 (a) Let x equal advertising expenditures (in thousands of dollars) and y equal revenue (in thousands of dollars). Use the method of least squares to develop a straight line approximation of the relationship between the two variables. (Round your numerical values to two decimal places.) (b) Test whether revenue and advertising expenditures (both in thousands of dollars) are related at a 0.05 level of significance. (Use the F test.) State the null and alternative hypotheses. Ho : Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. ---Select--- |H . We ---Select--- |conclude that the relationship between advertising expenditures and revenue (both in thousands of dollars) ---Select--- |significant.(c) Prepare a residual plot of y - y versus y. Use the result from part (a) to obtain the values of y. 15 15 15 10 10 10 5 5 Residuals Residuals Residuals 0 0 O -5 -5 -5 -10 -10+ -10 15 -15 -15 25 35 45 55 65 25 35 45 55 65 25 35 45 55 65 O Predicted Values Predicted Values Predicted Values 15 10 Residuals O -5 -10 -15 25 35 45 55 65 O Predicted Values (d) What conclusions can you draw from residual analysis? The plot suggests a ---Select--- in the residuals indicating that the assumption of a linear relationship x and y ---Select-- |satisfied. Should this model be used, or should we look for a better one? If this model is being used to predict values within the given range of data, this model ---Select--- adequate as the relationship ---Select--- | significant at the a = 0.05 level of significance. If this model is being used to extrapolate beyond the range of the data, this model ---Select--- adequate due to the nature of the residual analysis