We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2. HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Adrian Beltre 104 32 18.000 Justin Smoak 34 14 3.900 Jean Segura 64 20 2.600 Justin Upton 87 31 22.125 Brandon Crawford 84 12 6.000 Curtis Granderson 59 30 16.000 Aaron Hill 38 10 12.000 Miquel Cabrera 108 38 28.050 Adrian Gonzalez 90 18 21.857 Jacoby Ellsbury 56 9 21.143 Mark Teixeira 44 15 23.125 Albert Pujols 119 31 25.000 Matt Wieters 66 17 15.800 Logan Forsythe 52 20 2.750 Matt Kemp 108 35 21.500 Joey Votto 97 29 20.000 Victor Martinez 86 27 18.000 Prince Fielder 44 8 18.000 Shin-Soo Choo 17 7 20.000 Colby Rasmus 54 15 15.800 Evan Gattis 72 32 3.300 Brian McCann 58 20 17.000 Buster Posey 80 14 20.802 Denard Span 53 11 5.000 Jason Heyward 49 7 21.667 So you don't have to type all the data into the Reg2 sheet, you can copy the entire table and paste it into the Reg3 sheet or a new sheet. Then copy just the rows you need from the Reg3 sheet or the new sheet and paste them into the Reg2 sheet. a) Find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places. y^= + x1 + x2 b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 38 and HR of 19. Round your answer to 1 decimal place, do not convert numbers to dollars. millions of dollars c) Holding all other variables constant, what is the correct interpretation of the coefficient b1=0.1506 in the multiple linear regression equation? For each million dollars in salary, their RBIs should increase by 0.1506. For each RBI, a baseball player's predicted sallary increases by 0.1506 million dollars. If the baseball player's salary increases by 0.1506 million dollars, then the predicted RBI will increase by -0.1407. For each HR, a baseball player's predicted sallary increases by 0.1506 million dollars.
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.
We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2.
- HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error.
- RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error
- Salary is in millions of dollars.
The following is a chart of baseball players' salaries and statistics from 2016.
| Player Name | RBI's | HR's | Salary (in millions) |
|---|---|---|---|
| Adrian Beltre | 104 | 32 | 18.000 |
| Justin Smoak | 34 | 14 | 3.900 |
| Jean Segura | 64 | 20 | 2.600 |
| Justin Upton | 87 | 31 | 22.125 |
| Brandon Crawford | 84 | 12 | 6.000 |
| Curtis Granderson | 59 | 30 | 16.000 |
| Aaron Hill | 38 | 10 | 12.000 |
| Miquel Cabrera | 108 | 38 | 28.050 |
| Adrian Gonzalez | 90 | 18 | 21.857 |
| Jacoby Ellsbury | 56 | 9 | 21.143 |
| Mark Teixeira | 44 | 15 | 23.125 |
| Albert Pujols | 119 | 31 | 25.000 |
| Matt Wieters | 66 | 17 | 15.800 |
| Logan Forsythe | 52 | 20 | 2.750 |
| Matt Kemp | 108 | 35 | 21.500 |
| Joey Votto | 97 | 29 | 20.000 |
| Victor Martinez | 86 | 27 | 18.000 |
| Prince Fielder | 44 | 8 | 18.000 |
| Shin-Soo Choo | 17 | 7 | 20.000 |
| Colby Rasmus | 54 | 15 | 15.800 |
| Evan Gattis | 72 | 32 | 3.300 |
| Brian McCann | 58 | 20 | 17.000 |
| Buster Posey | 80 | 14 | 20.802 |
| Denard Span | 53 | 11 | 5.000 |
| Jason Heyward | 49 | 7 | 21.667 |
So you don't have to type all the data into the Reg2 sheet, you can copy the entire table and paste it into the Reg3 sheet or a new sheet. Then copy just the rows you need from the Reg3 sheet or the new sheet and paste them into the Reg2 sheet.
a) Find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places.
y^= + x1 + x2
b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 38 and HR of 19. Round your answer to 1 decimal place, do not convert numbers to dollars.
millions of dollars
c) Holding all other variables constant, what is the correct interpretation of the coefficient b1=0.1506 in the multiple linear regression equation?
- For each million dollars in salary, their RBIs should increase by 0.1506.
- For each RBI, a baseball player's predicted sallary increases by 0.1506 million dollars.
- If the baseball player's salary increases by 0.1506 million dollars, then the predicted RBI will increase by -0.1407.
- For each HR, a baseball player's predicted sallary increases by 0.1506 million dollars.
d) Holding all other variables constant, what is the correct interpretation of the coefficient b2=−0.1407 in the multiple linear regression equation?
- If the baseball player's salary increases by -0.1407 million dollars, then the predicted HR will increase by 0.1506.
- For each HR, a baseball player's predicted sallary increases by -0.1407 million dollars.
- For each RBI, a baseball player's predicted sallary increases by -0.1407 million dollars.
- For each million dollars in salary, a baseball player's HR will increase by -0.1407.
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