2 An ice cream vendor would like to predict daily sales of ice cream cones based on the temperature outdoors. Data for a random sam plc of 8 days are provided in the table below. 'l'cmperaturc (OC) Daily Sales (Litres) (x) (u) 6 135 8 50 12 125 16 100 18 200 22 150 28 250 28 175 The regression line with "daily sales" as the dependent variable and "temperature" as the independent variable has been calculated as: : 6} +- bg (fi rt. y=55217+5.38597x x/ 2 ii. in my. )25 7 = it You may use the following sums of squares and cross products for the questions below. y Zx=138 Zy=1185 SS" =495.5 SSyy = 26446.875 SSxy = 266875 2 marks a. Interpret the value of b in the sample regression line. What does it mean in the context of this question? 2 marks b. Compute the linear correlation between "daily sales" and "temperature." Note: Express your answer to 4 decimal places of accuracy. - mbmzr , 5:38'5'77376445/125 E ggzl'if7-7 H >< .Q l > u a b = SS'yxj/Stfixx = 2663'75 =53757gr77376(; Introduction to Statisticsthw 2 e,. "MM X ' our / mq-MOS k 'N s8 marks c. At the 5% significance level, can it be concluded that the between daily sales and tem appropriate hypotheses. Us correlation perature is positive? Formulate and test the e the critical value approach. 2 marks d. What percentage of the variation in daily sa les is explained by its linear relationship with temperature? 300 zro 7/ '200 Ko IO 0 So -'- OL ' + + 'l l g it? IS ia lg go X laura/ram"? r Whmt 2au In file 00wa 1} MM wyman, Hu (Mw all!) mj/IIZV/Vw' Wl fi 'L'w'v Wi M flu 7.53th [dal/ul M nw IQ flaw / / Mpa/mw maui MW". 5'3"? MWM Wit" fl/M Z/V edf'zl C b' 2 SSxy//J'Ss4x SYN/X/ -- 26457-75 '5 'L "' 4 Q 3 , n "vc on!" i I s "in... /v W I= Or]??? f/11 marks e. Using the regression line and sums of squares and cross products provided above, construct a 90% prediction interval for daily sales when the outside temperature is 24"C. m M ' OS:P/rv2 rv. :'/"'mvv,Y'T" FM, W . 'fwrr" ' Introduction to swam-cs