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Two statistical analysis tasks. The first task involves investigating the relationship between creativity scores and sales growth performance in a large company. The second task deals with predicting the number of calories in a fast-food menu item based on its fat content. Scatterplots, correlation coefficients, and regression equations.
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MATH 130: Worksheet 4 February 4th, 2010 Name: Show all work. Please answer neatly on an attached paper. Unsupported answers may receive no credit.
Creativity Score Sales Growth 9 93 7 89 8 95 13 101 10 102 10 96 9 95 18 111 10 103 14 107
We want to investigate if creative people tend to perform better with regard to sales growth. (a) Draw a scatterplot of the data. (Make sure to label the axis appropriately.) (b) Describe the form, direction, and strength of the relationship. (c) Find the correlation r between creativity score and sales growth. (d) What does this suggest about the association between creativity score and sales growth?
The equation of the least-squares regression line is: Calories = 204 + 11.4x (Fat)
The correlation between Calories and Fat is r = .979. Hence, r^2 = .958. Finally, the average number of calories in menu items is 663, and the average fat content in menu items is 40 grams. (a) We might feel comfortable using the least-squares regression equation to predict calories for a menu item having fat content in what range?
(b) The least-squares line would predict that a menu item with 40 grams of fat would have how many calories?
(c) What % of the variation in calories for menu items is explained by the regression on Fat content? (d) What is the residual corresponding to the value marked by *? [Assume this point is at (43 g, 850 cal) ]
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