Question

TACOS! You know who doesn't love tacos? Nobody Elliot loves tacos so much, he opened a taco stand. Like yourself, Elliot is a clever businessperson who wants to harness the power of statistics to maximize his profit. He collected some data on the products he sells. The following data represent the number of delicious goodies sold per day at Elliot's World Tacos and their prices. Price (x) Units sold (y) Item (just here for funsies, you won't use these names in your calculations) Beef taco Chicken taco Veggie taco Taco salad Chips & salsa Soda (mostly Granica) $3 $4 $6 $9 $2 $1 53 31 12 17 60 71 a. Develop a least-squares regression line and explain what the slope of the line indicates. b. Compute the coefficient of determination and comment on the strength of relationship between x and y. C. Compute the sample correlation coefficient between the price and the number of food items sold

PLEASE SHOW WORK ON EACH ONE.

Answer 1

(0) Let the negression line is regression line is Y = Bot B, nit E; = Bot Ba; the estimated the y- intercept B 11 ΣΥ, ΣΥ, Ix; - (2x)" 10491 3224 x 78 9 70 4872 - 10394176 10 -0.00169 -0.0017. the slope parameter = Y 8, 5 = 7.8 -0.0017x 322-4 z 7.252,

Here a is estimated by and ß is estimated ly b. b = I Y; Ni 5Y; IX Exi- &x;)" n a- r- bn 699 - 25 X 244 6 11 704163 147 ô 25 6 a 400 6.6Ť + 7.4163 X 4.1667 71.568. so the estimated line is Y 71.568 - 7. 4163 n; the interpretation of the slope. >. The a vennage decrease of y variable is 7o4163 unit bar unit Serca increment of x variable, pen b. the coebbicient of deternination is (R² R² w= n (Exy) - (5x) (») In 2x - (EX) - Unsyr-(tyje 6 x 699 244 x 25 C6X147 625),/ 6 X 12844 – 59536) O. 8064

у is 0.8064 It indicates that the variation of proportion ob variable which is related to the independent variable X according to the regression line It indicates this regression is good bit bor this dataset. sl sample correlation coebb. b = -1 -0.8980 the x § Ý [AS are negatively and strongley correlated]

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