Question

What is the relationship between the attendance at a major league ball game and the total number of ruins sored Attendance figures in thousands and the runs scored for randomly selected games are shown Attendance 15 20 21 5212 23 10 32 13 Runs 8 7 0 13 3 2310 9 .. Find the correlation coefficient: - Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: ROO The p-value is Pound to four decimal places c. Use a level of significance of a -0.05 to state the conclusion of the hypothesis test in the context of the study There is statistically significant evickice to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful There is statistically insig vificant evidence to conclude that there is a correlation between the Attendance of haseball games and the runs scored. The the use of the regression line is not appropriate There is statistically significant evidence to conclude that a game with higher attendance will have fewern.ns scored than a game with lower attendance There is statistically significant evidkace to conclude that a game with a higher attendance will have more uns scored than age with lower attendance (und to two decimal plexes) found to two decimal places) e Interpret: There is a chance that the regression line will be a good predictor for the runs scared based on the attendance of the game. Given any tid attendance, 64% of all of those games will have the predicted number of runs scored. 645 of all games will have the average number of runs scored. There is a large variation in the runs scored in baseball games, but if you only look at games with afted attendance, this variation on average is reduced by 0-13 1. The equation of the linear regression line is: Please show your answers to two decimal places 9. Use the model to predict the runs scared at a game that has an attendance af 27.con people. Please round your arswer tate rearest whole number.) h. Interpret the slope of the regression line in the context of the question: As goes by pes up. For every additional thousand cople who attend a game, there tends to be an average increase of 0.19 .ns scored. The slope has no practical meaning since the total number runs scored in a game must be positive i. Interpret the y-intercept in the context of the cuestion The best prediction for a game with attendance that there will be nuns scored. If the attendance of a baseball game is U, then 3 runs will be socred. The average runs scored is predicted to be They intercept has no practical meaning for this study

Answer 1

attendance runs 15 8 SUMMARY OUTPUT 26 7 21 9 52 13 12 3 Regression Statistics Multiple R 0.8012 R Square 0.6419 Adjusted R Square 0.5908 Standard Error 2.0425 Observations 9 23 8 16 3 32 10 43 9 ANOVA df SS MS 52.3539 F Significance F 12.5499 0.0094 1 Regression Residual Total 52.3539 29.2017 7 4.1717 8 81.5556 t Stat Lower 95% Coefficients Standard Error 2.7072 1.5850 1.7080 P-value 0.1314 0.0094 Intercept attendance -1.0407 Upper 95% 6.4551 0.3171 0.1901 0.0537 3.5426 0.0632

### Answers:

a] r = 0.80

b] H0: ρ= 0 ( rho=0)

H1 : ρ ≠ 0(rho not equal to 0)

p-value is 0.0094

c] second option is correct

d] r2 = 0.64

e] first option is correct

f] y^ =2.71 +0.19x

g]y^ =2.71 +0.19*27 =7.84 = 8 runs scored

h] second option is correct

i]first option is correct