Question

X 1 2 0.0 Most restaurants offer free refills for its customers who purchase a fountain soft drink. A certain buffet restaurant currently doesn't. But, it has been argued that customers who drink more soft drinks tend to eat less and, thus, cost the restaurant less for the meal the customer eats. To test this argument, this restaurant offered free refills to a sample of 6 of its customers. The total number of glasses each customer drank, X, and the $ cost of the meal each ate, Y, were recorded. The findings along with some additional calculations appear in the following table. Customer у X-X y-y (x - x)2 (y-7)(x-x)(y-7) 10 -0.5 2 0.25 4 - 1.0 2 1 8 - 1.5 0 2.25 0 3 6 0.5 -2 0.25 4 - 1.0 13 - 2.5 5 6.25 25 - 12.5 5 1.5 - 2 2.25 - 3.0 6 5 2.5 - 3 6.25 9 - 7.5 15 48 0 0 17.50 46 - 25.0 Using the above results, determine the following. ** Note: Please Show your work and highlight your final answers either with a highlighter or by placing a box around it so I understand and please Calculate all values to 4 decimal places.) DO NOT ANSWER THE FOLLOWING PARTS BY RUNNING EXCEL'S 'Regression'ANALYIS TOOL.** a) The standard deviation of Y 4 3 0 4 6 4 5 b) The standard deviation of X c) The correlation coefficient between X and Y d) The slope of the regression line expressing the linear relationship between cost and number of glasses e) The y-intercept of this regression line f) R2

Question Cont'd

Answer 1

that izi izi 6. Solm: Here in the data we have given that x + the total number of glasses each Customer drank Y Cost of the meal each ate In the table we have given X'= 15, EX;= 48 Ex-7)=0, Elyi-y)=0 E(0-3) 17:50 , £ 105-71*=46 É(Qc-) (95-7) --25.0 the above information We have provided @) atandard deviation gy S.D. i 121 (2) n lai (value put from table) て 127 で 17.67= 2.76947 S.D. = 7x96 S.D. fyz 12 2.7695 (6) S.D. of sögn +/x85 - 5.D-9X= 1.7078

© Correlation coeft between X andy (wele know that) r= Cov(xiu) (S.D-opy9x(SD_004) Cov (x,y) = x ² (xi-x) Cyi-g) (zi h Cov(x1y) = -25 So re - 25 x ) 2.7695 1-7078 18= -0.8809 @ the slobe y the regression line expressing the linear Lelationutlip between Cost cy) and number oglases (X) Since we know that slope of Line of regression you x is donated b, c'e, Con(x4) b= 82 6X (1.70782 Coxz (50.8 x 8) b=1.4286 (1) The y-intercept of this regression line 30 Now first we solve regression line you x which we know that b = 25

48 6. 28 łz ew 121 こ 14-] = b(x-3) (4-8)=1.5(X-905) Y-82 1.5%-3.75 to 14 = 1:5X +5.75 So Intercept of y, lil, on y ana's ,x=0 15 6 14 = 5.75