Question

STAT 1350 Homework Chapters 14-15 Name The price charged for a 16 ounce soda at Major League Baseball games depends on the price charged for a hot dog. The table below gives data for 21 Major League Stadiums, TABLE 14.2 Hot dog and soda pricos (in dollars) at Major League Baseball stadiums Team Hot dog Soda Team Hot dog Soda Team Hot dog Soda 2.75 Angels 2.29 Giants 3.75 3.00 2.25 Rangers 2.25 Astros 4.00 2.86 Indians 2.50 3.00 Red Sox 3.75 2.86 Braves 3.75 2.80 Marlins 8.00 2.67 Rockies 8.25 8.00 Brewers 2.50 2.67 Mets 4.60 2.85 Royals 2.50 2.29 Cardinals 3.00 3.14 Padres 3.00 3.00 Tigers 1.60 2.00 Dodgers 3.75 2.50 Phillies 3.25 2.40 3.00 2.20 Expos 1.47 2.20 Pirates 2.25 2.25 White Sox 2.75 2.67 Twins a) The explanatory variable is and the response variable is b) Make a scatterplot of the data. Label both axes with the appropriate measure (not just x and y). 2 3 c) Describe the direction, form, and strength of the relationship. direction strength d) Determine the correlation coefficient, r.

Answer 1

Sample size: 21 Mean x (x): 2.9795238095238 Mean y (ū): 2.5952380952381 Intercept (a): 1.8989415765267 Slope (b): 0.23369389312672 Regression line equation: y=1.8989415765267+0.23369389312672x 24 x 1.5 2 2.5 3 3.5 4 4.5 Use the linear regression equation to estimate y: Enter a value for x: 3.50 Calculate y y=2.71687020247022

Also, the following calculations are needed to compute the correlation coefficient: Х X*Y X2 y? 2.75 2.29 6.2975 7.5625 5.2441 4.00 2.86 11.44 16 8.1796 3.75 2.80 10.5 14.0625 7.84 2.50 2.67 6.675 6.25 7.1289 3.00 3.14 9.42 9 9.8596 3.75 2.50 9.375 14.0625 6.25 1.47 2.20 3.234 2.1609 4.84 3.75 3.00 11.25 14.0625 2.50 3.00 7.5 6.25 9 3.00 2.67 8.01 7.1289 4.50 2.55 11.475 20.25 6.5025 3.00 3.00 9 3.25 2.40 7.8 10.5625 5.76 2.25 2.25 5.0625 5.0625 5.0625 2.25 2.25 5.0625 5.0625 5.0625 3.75 2.86 10.725 14.0625 8.1796 3.25 3.00 9.75 10.5625 9 2.50 2.29 5.725 6.25 5.2441 1.60 2.00 3.2 2.56 4 3.00 2.20 6.6 4.84 2.75 2.57 7.0675 7.5625 6.6049 143.727 Sum = 62.57 54.5 165.169 198.345 9

The correlation coefficient r is computed using the following expression: d)2 r = SSxy VSSxx SSyy where SS ssx = 3x2++ (2x) (8) $$x = 3x - (3x) i=1 In this case, based on the data provided, we get that SSxy = 165.169 - ) (62.57 x 54.5) = 2.785 sSxx = 198.346 – 2 (62.57)2 = 11.917 SSyy = 143.727 - (54.5)2 = 2.287 Therefore, based on this information, the sample correlation coefficient is computed as follows SSXY SSXY_ = 2.785 11.917 x 2.287 = 0.533 VSSXXSSyy which completes the calculation.

The independent variable is Hotdog, and the dependent variable is Soda. In order to compute the regression coefficients, the following table needs to be used: Hot dog*Sod Hot dog Soda Hot dog? Soda2 2.75 2.29 6.2975 7.5625 5.2441 4.00 2.86 11.44 16 8.1796 3.75 2.80 10.5 14.0625 7.84 2.50 2.67 6.675 6.25 7.1289 3.00 3.14 9.42 9 9.8596 3.75 2.50 9.375 14.0625 6.25 1.47 2.20 3.234 2.1609 4.84 3.75 3.00 11.25 14.0625 2.50 7.5 6.25 3.00 2.67 3.00 8.01 9 7.1289 4.50 2.55 11.475 20.25 6.5025 3.00 3.00 9 3.25 2.40 7.8 10.5625 5.76 2.25 2.25 5.0625 5.0625 5.0625 2.25 2.25 5.0625 5.0625 5.0625 3.75 2.86 10.725 14.0625 8.1796 3.25 3.00 9.75 10.5625 9 2.50 2.29 5.725 6.25 5.2441 1.60 2.00 3.2 2.56 4. 3.00 2.20 6.6 9 4.84 2.75 2.57 7.0675 7.5625 6.6049 198.345 Sum = 62.57 54.5 165.169 143.727 2

Based on the above table, the following is calculated: 62.57 * = { x = 12:57 – 2,078528805:28 f)2 = 2.9795238095238 21 54.5 = 2.5952380952381 21 SSxx = = 198.3459 – 62. = 11.917095238095 $$x = ŻY? -- (3x) = 143.7272 – 5.5/21 = .2867235096237 Ssxy = Şxy -(Ex) (Y) = 165.160 – 62.57 x 54,5/21 = 2.784 i= 1 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows: mSSxy 2.7849523809523 = 0.2337 SSxx 11.917095238095 m = n = 7 - 7. m = 2.5952380952381 – 2.9795238095238 x 0.2337 = 1.8989 Therefore, we find that the regression equation is: Soda = 1.8989 + 0.2337Hotdog Graphically: Scatter Plot and Regression Line 3.37 3.17 2.97 mi ma posia 2.77 1.97 1.77.86 1.36 1.86 2.36 2.86 3.36 3.86 4.36 4.86 Hot dog - Regression equation: Y = 1.8989 + 0.2337* X

co Direction - Positive Association - Because as hot dog incocases So does soda. • Form - Linear Relation Points on scatteoplot closely resemble a streght line. o gbength - Moderate When coorelation coefficient jg betuoees 0.5 -0.7 thes stength of selationship is moderate 9 7 = 1.8989+ 0.2337 * 3.50 y = 2.7169 b) y = 1.8989 + 0.2337 * 7.50 y = 3.6516
Its a regression problem and interpret form , strength , direction.