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 DETAILED WORK ON EACH ANSWER

Answer 1

Solution: $6 $9 $2 Price cx); $3 $4 $1 Units sold(y): 53 31 12 17 60 71 (1 Develop a least squares regression line and explain what the slope of the line indicates. Aneill least square regrasion Time is given by- a + b X where Y = Units sold X = Price (in dollars) a = Intercept b= slope Y = X2 2 16 Х ху 3 53 159 4 31 124 6 12 72 9 153 2 60 120 71 케 Ex=25 Ey=244 EXy=699 36 81 Y 2809 961 144 289 3600 504/ 17 प EX?147 Ey=12844 n=6, EX= 25, EY= 244 EXY = 699 EX²= 147 Ey?. 12844

Slope = b = SSxy SSxx where, SSxx = EX-1 (EX = 147 - (25) ń (Ex)? L 9 = 147 - 625 = 147 – 104.17 9 42.83 SSxy= 42.83 SSxy = EXY - 5 (EX) (EY) 699 L x 25 x 244 6 = 699 - 1016.67 = -317.67 SSxy=-317.67 b= 317.67 42.83 -7.417 Slope (b) = -7.417

now, where y = LEY Inter cept (a) is given by a= y - bT 244 244 40-67 X = LEX 25 4.17 6 n a = 40.67 -(-7.417) x 4.17 40.67 t 30.929 71.60 la= 71.60 Regression equation is : Units sold = 71.60 - 7.417 Price Interpret the slope: If the price is increases by 1 dollar, we predict the Units sold will decrease by approximately 7.417

FLEX-KLASY (c) Compute the sample correlation coefficient between the price @) and number of food items Soldly) Ans Correlation (8) is defined as 7= exy - XT 7x699 = _4.J7X 40.67 Fx147-[4-17] 4*42844-[406779 6 116.5 169.5939 |(29.5=1*.3889) (21470.67–15v.oven - 53.0939 7.IT*48606217 - 53,0939 3460-44113 -0.9026 -53,0939 58.8253 correlation 0.9026 This is strong regative correlation between Xty.

i's (b) Coefficient of Determination (R2) Squared value of correlation called coefficient of determination (R2) R2= (0.9026) = 0.8147 It means 81.47% CAPprox) of the Variation in Unit Sold (y) is explained explained by Price (X),