Question

Refer to the Baseball 2016 data, which reports information on the 2016 Major League Baseball season. Let attendance be the dependent variable and total team salary be the independent variable. Determine the regression equation and answer the following questions.

Draw a scatter diagram. From the diagram, does there seem to be a direct relationship between the two variables?

What is the expected attendance for a team with a salary of $100.0 million?

If the owners pay an additional $30 million, how many more people could they expect to attend?

At the .05 significance level, can we conclude that the slope of the regression line is positive? Conduct the appropriate test of hypothesis.

What percentage of the variation in attendance is accounted for by salary?

Determine the correlation between attendance and team batting average and between attendance and team ERA. Which is stronger? Conduct an appropriate test of hypothesis for each set of variables.

Show all work in Excel

Team	League	Year Opened	Team Salary	Attendance	Wins	ERA	BA	HR			Year	Average salary
Arizona	National	1998	65.80	2080145	79	4.04	0.264	154			2000	1988034
Atlanta	National	1996	89.60	2001392	67	4.41	0.251	100			2001	2264403
Baltimore	American	1992	118.90	2281202	81	4.05	0.250	217			2002	2383235
Boston	American	1912	168.70	2880694	78	4.31	0.265	161			2003	2555476
Chicago Cubs	National	1914	117.20	2959812	97	3.36	0.244	171			2004	2486609
Chicago Sox	American	1991	110.70	1755810	76	3.98	0.250	136			2005	2632655
Cincinnati	National	2003	117.70	2419506	64	4.33	0.248	167			2006	2866544
Cleveland	American	1994	87.70	1388905	81	3.67	0.256	141			2007	2944556
Colorado	National	1995	98.30	2506789	68	5.04	0.265	186			2008	3154845
Detroit	American	2000	172.80	2726048	74	4.64	0.270	151			2009	3240206
Houston	American	2000	69.10	2153585	86	3.57	0.250	230			2010	3297828
Kansas City	American	1973	112.90	2708549	95	3.73	0.269	139			2011	3305393
LA Angels	American	1966	146.40	3012765	85	3.94	0.246	176			2012	3440000
LA Dodgers	National	1962	230.40	3764815	92	3.44	0.250	187			2013	3650000
Miami	National	2012	84.60	1752235	71	4.02	0.260	120			2014	3950000
Milwaukee	National	2001	98.70	2542558	68	4.28	0.251	145			2015	4250000
Minnesota	American	2010	108.30	2220054	83	4.07	0.247	156
NY Mets	National	2009	100.10	2569753	90	3.43	0.244	177
NY Yankees	American	2009	213.50	3193795	87	4.05	0.251	212
Oakland	American	1966	80.80	1768175	68	4.14	0.251	146
Philadelphia	National	2004	133.00	1831080	63	4.69	0.249	130
Pittsburgh	National	2001	85.90	2498596	98	3.21	0.260	140
San Diego	National	2004	126.60	2459742	74	4.09	0.243	148
San Francisco	National	2000	166.50	3375882	84	3.72	0.267	136
Seattle	American	1999	123.20	2193581	76	4.16	0.249	198
St. Louis	National	2006	120.30	3520889	100	2.94	0.253	137
Tampa Bay	American	1990	74.80	1287054	80	3.74	0.252	167
Texas	American	1994	144.80	2491875	88	4.24	0.257	172
Toronto	American	1989	116.40	2794891	93	3.8	0.269	232
Washington	National	2008	174.50	2619843	83	3.62	0.251	177

Answer 1

Solution:

Required regression model by using excel is given as below:

Regression Statistics
Multiple R	0.706773855
R Square	0.499529282
Adjusted R Square	0.481655328
Standard Error	427738.1077
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5.11324E+12	5.11324E+12	27.94732921	1.26761E-05
Residual	28	5.12288E+12	1.8296E+11
Total	29	1.02361E+13
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1196918.806	251124.0645	4.766244957	5.25468E-05	682514.4856	1711323.126
Team Salary	10347.28988	1957.295783	5.286523357	1.26761E-05	6337.951267	14356.62848

Determine the regression equation and answer the following questions.

Attendance = 1196918.806 + 10347.28988*Team salary

Y = 1196918.806 + 10347.28988*X

Draw a scatter diagram. From the diagram, does there seem to be a direct relationship between the two variables?

Scatter diagram is given as below:

From above scatter diagram, it is observed that there is moderate positive linear relationship exists between the two variables.

What is the expected attendance for a team with a salary of $100.0 million?

Attendance = 1196918.806 + 10347.28988*Team salary

Attendance = 1196918.806 + 10347.28988*100

Attendance = 2231647.794

If the owners pay an additional $30 million, how many more people could they expect to attend?

Attendance = 1196918.806 + 10347.28988*Team salary

Attendance = 1196918.806 + 10347.28988*130

Attendance = 2542066.49

At the .05 significance level, can we conclude that the slope of the regression line is positive? Conduct the appropriate test of hypothesis.

H₀: β = 0 versus H_a: β > 0

We are given α = 0.05

β̂ = 10347.28988

SE =    1957.295783

t = β̂/SE = 10347.28988/1957.295783

t = 5.286523357

P-value = 0.00

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the slope of regression line is positive.

What percentage of the variation in attendance is accounted for by salary?

WE are given coefficient of determination or the value of R square is given as 0.499529282, which means about 50.0% of the variation in attendance is accounted for by salary.

Determine the correlation between attendance and team batting average and between attendance and team ERA. Which is stronger? Conduct an appropriate test of hypothesis for each set of variables.

Correlation coefficient between attendance and team batting average = 0.124065

Correlation coefficient between attendance and team ERA = -0.30198

Correlation coefficient between attendance and team ERA is stronger than Correlation coefficient between attendance and team batting average.