Question

1. 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 O' 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 Grapico) $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

Answer 1

X - My Y - My -1.167 -0.167 1.833 4.833 -2.167 -3.167 12.333 -9.667 28.667 -23.667 19.333 30.333 (X - Myj2 1.361 0.028 3.361 23.361 4.694 10.028 (Y - My)? 152.111 93.444 821.778 560.111 373.778 920.111 (X - Mx)(Y - My) -14.389 1.611 -52.556 -114.389 -41.889 -96.056 Mx: 4.167 My: 40.667 Sum: 42.833 Sum: 2921.333 Sum: -317.667

7 = bxc tu Here Moc=se= sa 0 A least -square Regression Line My=9=smanu, 40.64 b= (x-Mac) G - My) (a-Mocje - 4.16 317.66 42,83 -7.42 = My a b Moc I 40.67 - 69.42 x 4016) 71.56 .: Y - 7.420 + 71.56 The slope indlicates nagative Relation.

2 Coefficient of determination=r ra {(o-Mac) (y-My) {(o-Mac)? {Cy-My)? 317.667 42183)921:33) - 317.667 353.723 0.898 .in p² (-0.898) 2 0.806 Its strong Relutionship between x andy Correlation coefficient r r = -0.8987 (we have already calculated)