Refer to the Baseball 2018 data, which reports information on the 2018 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. Click here for the Excel Data File Team Salary Year Stadium Opened Attendance Net Worth League ($ mil) HR BA Wins ERA mil $ bil National 143.32 176 0.235 82 3.72 1998 2.242695 1.21 National 130.6 175 0.257 90 3.75 2017 2.555781 1.625 American 127.63 188 0.239 47 5.18 1992 1.564192 1.2 American 227.4 208 0.268 108 3.75 1912 2.895575 2.8 National 194.26 167 0.258 95 3.65 1914 3.181089 2.9 American 71.84 182 0.241 62 4.84 1991 1.608817 1.5 National 100.31 172 0.254 67 4.63 2003 1.629356 1.01 American 142.8 216 0.259 91 3.77 1994 1.926701 1.045 National 143.97 210 0.256 91 4.33 1995 3.01588 1.1 American 130.96 135 0.241 64 4.58 2000 1.85697 1.225 American 163.52 205 0.255 103 3.11 2000 2.980549 1.65 American 129.94 155 0.245 58 4.94 1973 1.665107 1.015 American 173.78 214 0.242 80 4.15 1966 3.020216 1.8 National 199.58 235 0.25 92 3.38 1962 3.8575 3 National 91.82 128 0.237 63 4.76 2012 0.811104 1 National 108.98 218 0.252 96 3.73 2001 2.850875 1.03 American 115.51 166 0.25 78 4.5 2010 1.959197 1.15 National 150.19 170 0.234 77 4.07 2009 2.224995 2.1 American 179.6 267 0.249 100 3.78 2009 3.482855 4 American 80.32 227 0.252 97 3.81 1966 1.573616 1.02 National 104.3 186 0.234 80 4.14 2004 2.158124 1.7 National 91.03 157 0.254 82 4 2001 1.465316 1.26 National 101.34 162 0.235 66 4.4 2004 2.168536 1.27 American 205.67 176 0.254 89 4.13 2000 2.299489 2.85 National 160.99 133 0.239 73 3.95 1999 3.156185 1.45 National 163.78 205 0.249 88 3.85 2006 3.403587 1.9 American 68.81 150 0.258 90 3.74 1990 1.154973 0.9 American 140.63 194 0.24 67 4.92 1994 2.107107 1.6 American 150.95 217 0.244 73 4.85 1989 2.325281 1.35 National 181.38 191 0.254 82 4.04 2008 2.529604 1.675 d-2. State the decision rule. (Round your answer to 3 decimal places.) d-3. Compute the value of the test statistic. Use the 0.05 significance level. (Round your answer to 4 decimal places.) d-4. What is your decision regarding H0? d-5. Can we conclude that the slope of the regression line is positive? multiple choice 3 Yes No e. What percentage of the variation in attendance is accounted for by salary? (Round your answer to 2 decimal places.) f-1. Determine the correlation between attendance and team batting average and between attendance and team ERA. (Negative amount should be indicated by a minus sign. Round your answers to 4 decimal places.) f-2 Which has a stronger correlation between the variables? f-3. State the null and alternate hypotheses for attendance and batting. multiple choice 4 H0: ρ = 0 and H1: ρ < 0 H0: ρ > 0 and H1: ρ ≤ 0 H0: ρ < 0 and H1: ρ ≥ 0 H0: ρ ≤ 0 and H1: ρ > 0 f-4. State the decision rule. Use the 0.05 significance level.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Refer to the Baseball 2018 data, which reports information on the 2018 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.
Click here for the Excel Data File
| Team Salary | Year Stadium Opened | Attendance | Net Worth | |||||
| League | ($ mil) | HR | BA | Wins | ERA | mil | $ bil | |
| National | 143.32 | 176 | 0.235 | 82 | 3.72 | 1998 | 2.242695 | 1.21 |
| National | 130.6 | 175 | 0.257 | 90 | 3.75 | 2017 | 2.555781 | 1.625 |
| American | 127.63 | 188 | 0.239 | 47 | 5.18 | 1992 | 1.564192 | 1.2 |
| American | 227.4 | 208 | 0.268 | 108 | 3.75 | 1912 | 2.895575 | 2.8 |
| National | 194.26 | 167 | 0.258 | 95 | 3.65 | 1914 | 3.181089 | 2.9 |
| American | 71.84 | 182 | 0.241 | 62 | 4.84 | 1991 | 1.608817 | 1.5 |
| National | 100.31 | 172 | 0.254 | 67 | 4.63 | 2003 | 1.629356 | 1.01 |
| American | 142.8 | 216 | 0.259 | 91 | 3.77 | 1994 | 1.926701 | 1.045 |
| National | 143.97 | 210 | 0.256 | 91 | 4.33 | 1995 | 3.01588 | 1.1 |
| American | 130.96 | 135 | 0.241 | 64 | 4.58 | 2000 | 1.85697 | 1.225 |
| American | 163.52 | 205 | 0.255 | 103 | 3.11 | 2000 | 2.980549 | 1.65 |
| American | 129.94 | 155 | 0.245 | 58 | 4.94 | 1973 | 1.665107 | 1.015 |
| American | 173.78 | 214 | 0.242 | 80 | 4.15 | 1966 | 3.020216 | 1.8 |
| National | 199.58 | 235 | 0.25 | 92 | 3.38 | 1962 | 3.8575 | 3 |
| National | 91.82 | 128 | 0.237 | 63 | 4.76 | 2012 | 0.811104 | 1 |
| National | 108.98 | 218 | 0.252 | 96 | 3.73 | 2001 | 2.850875 | 1.03 |
| American | 115.51 | 166 | 0.25 | 78 | 4.5 | 2010 | 1.959197 | 1.15 |
| National | 150.19 | 170 | 0.234 | 77 | 4.07 | 2009 | 2.224995 | 2.1 |
| American | 179.6 | 267 | 0.249 | 100 | 3.78 | 2009 | 3.482855 | 4 |
| American | 80.32 | 227 | 0.252 | 97 | 3.81 | 1966 | 1.573616 | 1.02 |
| National | 104.3 | 186 | 0.234 | 80 | 4.14 | 2004 | 2.158124 | 1.7 |
| National | 91.03 | 157 | 0.254 | 82 | 4 | 2001 | 1.465316 | 1.26 |
| National | 101.34 | 162 | 0.235 | 66 | 4.4 | 2004 | 2.168536 | 1.27 |
| American | 205.67 | 176 | 0.254 | 89 | 4.13 | 2000 | 2.299489 | 2.85 |
| National | 160.99 | 133 | 0.239 | 73 | 3.95 | 1999 | 3.156185 | 1.45 |
| National | 163.78 | 205 | 0.249 | 88 | 3.85 | 2006 | 3.403587 | 1.9 |
| American | 68.81 | 150 | 0.258 | 90 | 3.74 | 1990 | 1.154973 | 0.9 |
| American | 140.63 | 194 | 0.24 | 67 | 4.92 | 1994 | 2.107107 | 1.6 |
| American | 150.95 | 217 | 0.244 | 73 | 4.85 | 1989 | 2.325281 | 1.35 |
| National | 181.38 | 191 | 0.254 | 82 | 4.04 | 2008 | 2.529604 | 1.675 |
d-2. State the decision rule. (Round your answer to 3 decimal places.)
d-3. Compute the value of the test statistic. Use the 0.05 significance level. (Round your answer to 4 decimal places.)
d-4. What is your decision regarding H0?
d-5. Can we conclude that the slope of the regression line is positive?
multiple choice 3
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Yes
-
No
e. What percentage of the variation in attendance is accounted for by salary? (Round your answer to 2 decimal places.)
f-1. Determine the
f-2 Which has a stronger correlation between the variables?
f-3. State the null and alternate hypotheses for attendance and batting.
multiple choice 4
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H0: ρ = 0 and H1: ρ < 0
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H0: ρ > 0 and H1: ρ ≤ 0
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H0: ρ < 0 and H1: ρ ≥ 0
-
H0: ρ ≤ 0 and H1: ρ > 0
f-4. State the decision rule. Use the 0.05 significance level. (Round your answer to 3 decimal places.)
f-5. Compute the value of the test statistic. (Round your answer to 4 decimal places.)
f-6. What is your decision regarding H0?
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Refer to the Baseball 2018 data, which reports information on the 2018 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.
Click here for the Excel Data File
a-1. Draw a
1. On the graph below, use the point tool to plot the point corresponding to the Attendance and its team salary (Salary 1).
2. Repeat the process for the remainder of the sample Salary 2, Salary 3, … ).
3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.
a-2. From the diagram, does there seem to be a direct relationship between the two variables?
multiple choice 1
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Yes
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No
b. What is the expected attendance for a team with a salary of $100.0 million? (Round your answer to 4 decimal places.)
c. If the owners pay an additional $30 million, how many more people could they expect to attend? (Round your answer to 3 decimal places.)
d-1. State the null and alternate hypotheses.
multiple choice 2
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H0: β = 0 and H1: β < 0
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H0: β > 0 and H1: β ≤ 0
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H0: β < 0 and H1: β ≥ 0
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H0: β ≤ 0 and H1: β > 0
d-2. State the decision rule. (Round your answer to 3 decimal places.)
d-3. Compute the value of the test statistic. Use the 0.05 significance level. (Round your answer to 4 decimal places.)
d-4. What is your decision regarding H0?
d-5. Can we conclude that the slope of the regression line is positive?
multiple choice 3
-
Yes
-
No
e. What percentage of the variation in attendance is accounted for by salary? (Round your answer to 2 decimal places.)
f-1. Determine the
f-2 Which has a stronger correlation between the variables?
f-3. State the null and alternate hypotheses for attendance and batting.
multiple choice 4
-
H0: ρ = 0 and H1: ρ < 0
-
H0: ρ > 0 and H1: ρ ≤ 0
-
H0: ρ < 0 and H1: ρ ≥ 0
-
H0: ρ ≤ 0 and H1: ρ > 0
f-4. State the decision rule. Use the 0.05 significance level. (Round your answer to 3 decimal places.)
f-5. Compute the value of the test statistic. (Round your answer to 4 decimal places.)
f-6. What is your decision regarding H0?
f-7. State the null and alternate hypotheses for attendance and ERA.
multiple choice 5
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H0: ρ = 0 and H1: ρ ≤ 0
-
H0: ρ ≥ 0 and H1: ρ < 0
-
H0: ρ > 0 and H1: ρ = 0
-
H0: ρ ≤ 0 and H1: ρ ≠ 0
f-8. State the decision rule. Use the 0.05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
f-9. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 4 decimal places.)
f-10. What is your decision regarding H0?
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