The accompanying data show the number of people working and the sales for a small bookstore. The regression line is given below. The bookstore decides to have a gala event in an attempt to drum up business. They hire 101 employees for the day and bring in a total of $40,000. Complete parts a through d below. Sales = 8.340 + 0.910 Number of Salespeople Working Click the icon to view the data table. a) Find the regression line predicting Sales from Number of people working with the new point added. Sales = + ()Number of Salespeople Working (Round to three decimal places as needed.) b) What has changed from the original regression equation? The intercept has ? and the coefficient for the Number of Salespeople Working has c) Is the new point a high leverage point or an influential point? The new point ? a high leverage point because d) Does the new point have a large residual? Explain. The residual of the new point is . (Round to two decimal places as needed.) ? The new point ? an influential point because Does the new point have a large residual? Explain. A. The new point has a large residual because the x-value is very close to the mean of the data set. B. The new point has a small residual. A high leverage and influential point does not need to have a large residual, since it pulls the regression line towards itself. C. The new point has a small residual because the x-value is very close to the mean of the data set. D. The new point has a large residual because it is an outlier. Bookstore data Full data set Number of Salespeople Working Sales (in $1000's) 2 11 3 11 7 13 9 14 10 19 11 21 12 20 14 20 17 23 20 27 x = 10.5 y = 17.9 SD(x) = 5.68 SD(y) = 5.40 X
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The retail sales of family clothing stores in the United States from 2009 through 2013 are shown in the table. The coefficients of the least squares regression parabola $y=a t^{2}+b t+c,$ where $y$ represents the retail sales (in billions of dollars) and $t$ represents the year, with $t=9$ corresponding to $2009,$ can be found by solving the system $\left\{\begin{array}{rr}80,499 a+6985 b+615 c= & 56,453.6 \\ 6985 a+615 b+55 c= & 5004.4 \\ 615 a+\quad 55 b+\quad 5 c= & 450.8\end{array}\right.$ (a) Use Cramer's Rule to solve the system and write the least squares regression parabola for the data. (b) Use a graphing utility to graph the parabola with the data. How well does the model fit the data? (c) Use the model to predict the retail sales of family clothing stores in the U.S. in the year 2015
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