Question

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The Los Angeles Dodgers have many devoted fans that pack the stadium for games (pre-COVID). The Dodgers record the number of attendees at their games (expressed in thousands). They also collect a wide range of different statistics from the game. The statistic that most fans are concerned about is the number of runs scored. Data from 12 randomly selected games are shown in the table below. What is the relationship between the attendance at the Los Angeles Dodgers games and the total number of runs scored? Attendance Runs 47 59 22 15 33 24 58 14 57 38 32 52 13 10 7 7 9 8 13 7 10 12 5 9 a. The null and alternative hypotheses for correlation are: H: ? = 0 H: 70 The p-value is: (Round to four decimal places) b. 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 evidence to conclude that there is a correlation between the attendance of Dodgers baseball games and the runs scored. Thus, the regression line is useful. There is statistically insignificant evidence to conclude that there is a correlation between the attendance of Dodgers baseball games and the runs scored. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a Dodgers game with higher attendance will have fewer runs scored than a game with lower attendance. There is statistically significant evidence to conclude that a Dodgers game with a higher attendance will have more runs scored than a game with lower attendance. c. Find the correlation coefficient: r = Round to 2 decimal places. d. 2 (Round to two decimal places) (Round to two decimal places)

Answer 1

We input the data set in Excel and use the "Regression" option under Data > Data Analysis to carry out this regression problem and answer the given questions. The output is given below. Here, x = Attendance, y = Runs.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6812
R Square	0.4641
Adjusted R Square	0.4105
Standard Error	1.9598
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	33.2591	33.2591	8.6595	0.0147
Residual	10	38.4076	3.8408
Total	11	71.6667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%
Intercept	5.2706	1.4398	3.6607	0.0044	2.0626	8.4786	2.0626
x	0.1037	0.0352	2.9427	0.0147	0.0252	0.1822	0.0252

(a) $H_0: \rho = 0$ , $H_1: \rho \ne 0$ . The p-value = P-value of x = 0.0147.
(b) 1st option.
(c) r = Multiple R = 0.68.
(d) r² = R Square = 0.46.
(e) 1st option.
(f) $\hat{y}$ = 5.27 + 0.10 .
(g) Runs scored = 5.27 + (0.10 * 34) = 8.795 = 9 runs (approx.) (or, 8 runs).
(h) 3rd option.
(i) 3rd option.