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

a)

X	Y	XY	XX	YY
3	53	159	9	2809
4	31	124	16	961
6	12	72	36	144
9	17	153	81	289
2	60	120	4	3600
1	71	71	1	5041

ΣΧ = 25, ΣΥ = 244, ΣΧ.Υ = 699, ΣΧ? = 147, ΣΥ? = 12844

α – ΣΥΣΧ? -ΣΧΣΧΥ η-ΣΧ2 - (ΣΧ)? Ξ 244 - 147 – 25 - 699 6. 147 – 252 71.568 6 = η-ΣΧΥ – ΣΧ.ΣΥ η-ΣΧ2 – (ΣΧ)? 6 - 699 – 25 - 244 6. 147 – (25) & –7.416

The regression equation is

ข = a + - 7 ข = 71.568 - 7.416 - 1

b)

η-ΣΧΥ – ΣΧ.ΣΥ r [ΣΧ? - (ΣΧ] - [n ΣΥ2 - (ΣΥ] Ο = r R -0.898 6 - 699 – 25 - 244 [6 - 14 [6 - 147 – 252] - [6 - 12844 – 2442]

The Coefficient is determination, r2 = (-0.898)2 = 0.806

Interpretation: There is 80.3% variation in (Units sold)y that is explained by the linear regression and by (Price)

c)

The sample Correlation coefficient, r = -0.898

There is negative association between price and units sold

that is price increases then units sold decreases and vice versa.