We wish to predict the salary for baseball players (yy) using the variables RBI (x1x1) and HR (x2x2), 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) Miquel Cabrera 108 38 28.050 Yoenis Cespedes 86 31 27.500 Ryan Howard 59 25 25.000 Albert Pujols 119 31 25.000 Robinson Cano 103 39 24.050 Mark Teixeira 44 15 23.125 Joe Mauer 49 11 23.000 Hanley Ramirez 111 30 22.750 Justin Upton 87 31 22.125 Adrian Gonzalez 90 18 21.857 Jason Heyward 49 7 21.667 Jayson Werth 70 21 21.571 Matt Kemp 108 35 21.500 Jacoby Ellsbury 56 9 21.143 Chris Davis 84 38 21.119 Buster Posey 80 14 20.802 Shin-Soo Choo 17 7 20.000 Troy Tulowitzki 79 24 20.000 Ryan Braun 91 31 20.000 Joey Votto 97 29 20.000 Hunter Pence 57 13 18.500 Prince Fielder 44 8 18.000 Adrian Beltre 104 32 18.000 Victor Martinez 86 27 18.000 Carlos Gonzalez 100 25 17.454 Matt Holliday 62 20 17.000 Brian McCann 58 20 17.000 Mike Trout 100 29 16.083 David Ortiz 127 38 16.000 Adam Jones 83 29 16.000 Curtis Granderson 59 30 16.000 Colby Rasmus 54 15 15.800 Matt Wieters 66 17 15.800 J.D. Martinez 68 22 6.750 Brandon Crawford 84 12 6.000 Rajai Davis 48 12 5.950 Aaron Hill 38 10 12.000 Coco Crisp 55 13 11.000 Ben Zobrist 76 18 10.500 Justin Turner 90 27 5.100 Denard Span 53 11 5.000 Chris Iannetta 24 7 4.550 Leonys Martin 47 15 4.150 Justin Smoak 34 14 3.900 Jorge Soler 31 12 3.667 Evan Gattis 72 32 3.300 Logan Forsythe 52 20 2.750 Jean Segura 64 20 2.600 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. ˆy=y^= + x1x1 + x2x2 b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 30 and HR of 21. Round your answer to 1 decimal place, do not convert numbers to dollars. millions of 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 (yy) using the variables RBI (x1x1) and HR (x2x2), 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) |
|---|---|---|---|
| Miquel Cabrera | 108 | 38 | 28.050 |
| Yoenis Cespedes | 86 | 31 | 27.500 |
| Ryan Howard | 59 | 25 | 25.000 |
| Albert Pujols | 119 | 31 | 25.000 |
| Robinson Cano | 103 | 39 | 24.050 |
| Mark Teixeira | 44 | 15 | 23.125 |
| Joe Mauer | 49 | 11 | 23.000 |
| Hanley Ramirez | 111 | 30 | 22.750 |
| Justin Upton | 87 | 31 | 22.125 |
| Adrian Gonzalez | 90 | 18 | 21.857 |
| Jason Heyward | 49 | 7 | 21.667 |
| Jayson Werth | 70 | 21 | 21.571 |
| Matt Kemp | 108 | 35 | 21.500 |
| Jacoby Ellsbury | 56 | 9 | 21.143 |
| Chris Davis | 84 | 38 | 21.119 |
| Buster Posey | 80 | 14 | 20.802 |
| Shin-Soo Choo | 17 | 7 | 20.000 |
| Troy Tulowitzki | 79 | 24 | 20.000 |
| Ryan Braun | 91 | 31 | 20.000 |
| Joey Votto | 97 | 29 | 20.000 |
| Hunter Pence | 57 | 13 | 18.500 |
| Prince Fielder | 44 | 8 | 18.000 |
| Adrian Beltre | 104 | 32 | 18.000 |
| Victor Martinez | 86 | 27 | 18.000 |
| Carlos Gonzalez | 100 | 25 | 17.454 |
| Matt Holliday | 62 | 20 | 17.000 |
| Brian McCann | 58 | 20 | 17.000 |
| Mike Trout | 100 | 29 | 16.083 |
| David Ortiz | 127 | 38 | 16.000 |
| Adam Jones | 83 | 29 | 16.000 |
| Curtis Granderson | 59 | 30 | 16.000 |
| Colby Rasmus | 54 | 15 | 15.800 |
| Matt Wieters | 66 | 17 | 15.800 |
| J.D. Martinez | 68 | 22 | 6.750 |
| Brandon Crawford | 84 | 12 | 6.000 |
| Rajai Davis | 48 | 12 | 5.950 |
| Aaron Hill | 38 | 10 | 12.000 |
| Coco Crisp | 55 | 13 | 11.000 |
| Ben Zobrist | 76 | 18 | 10.500 |
| Justin Turner | 90 | 27 | 5.100 |
| Denard Span | 53 | 11 | 5.000 |
| Chris Iannetta | 24 | 7 | 4.550 |
| Leonys Martin | 47 | 15 | 4.150 |
| Justin Smoak | 34 | 14 | 3.900 |
| Jorge Soler | 31 | 12 | 3.667 |
| Evan Gattis | 72 | 32 | 3.300 |
| Logan Forsythe | 52 | 20 | 2.750 |
| Jean Segura | 64 | 20 | 2.600 |
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.
ˆy=y^= + x1x1 + x2x2
b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 30 and HR of 21. Round your answer to 1 decimal place, do not convert numbers to dollars.
millions of dollars
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