Our data shows that a team with 49 wins has never missed the playoffs. What is the expected points difference for a team to make it to the postseason? Use the lecture solution file and more specifically the WinsReg model.

NBA <- read.csv("NBA_train.csv")
str(NBA)
## 'data.frame':    835 obs. of  20 variables:
##  $ SeasonEnd: int  1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 ...
##  $ Team     : chr  "Atlanta Hawks" "Boston Celtics" "Chicago Bulls" "Cleveland Cavaliers" ...
##  $ Playoffs : int  1 1 0 0 0 0 0 1 0 1 ...
##  $ W        : int  50 61 30 37 30 16 24 41 37 47 ...
##  $ PTS      : int  8573 9303 8813 9360 8878 8933 8493 9084 9119 8860 ...
##  $ oppPTS   : int  8334 8664 9035 9332 9240 9609 8853 9070 9176 8603 ...
##  $ FG       : int  3261 3617 3362 3811 3462 3643 3527 3599 3639 3582 ...
##  $ FGA      : int  7027 7387 6943 8041 7470 7596 7318 7496 7689 7489 ...
##  $ X2P      : int  3248 3455 3292 3775 3379 3586 3500 3495 3551 3557 ...
##  $ X2PA     : int  6952 6965 6668 7854 7215 7377 7197 7117 7375 7375 ...
##  $ X3P      : int  13 162 70 36 83 57 27 104 88 25 ...
##  $ X3PA     : int  75 422 275 187 255 219 121 379 314 114 ...
##  $ FT       : int  2038 1907 2019 1702 1871 1590 1412 1782 1753 1671 ...
##  $ FTA      : int  2645 2449 2592 2205 2539 2149 1914 2326 2333 2250 ...
##  $ ORB      : int  1369 1227 1115 1307 1311 1226 1155 1394 1398 1187 ...
##  $ DRB      : int  2406 2457 2465 2381 2524 2415 2437 2217 2326 2429 ...
##  $ AST      : int  1913 2198 2152 2108 2079 1950 2028 2149 2148 2123 ...
##  $ STL      : int  782 809 704 764 746 783 779 782 900 863 ...
##  $ BLK      : int  539 308 392 342 404 562 339 373 530 356 ...
##  $ TOV      : int  1495 1539 1684 1370 1533 1742 1492 1565 1517 1439 ...
NBA$PTSdiff = NBA$PTS - NBA$oppPTS
WinsReg = lm(W ~ PTSdiff, data=NBA)
summary(WinsReg)
## 
## Call:
## lm(formula = W ~ PTSdiff, data = NBA)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.7393 -2.1018 -0.0672  2.0265 10.6026 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.100e+01  1.059e-01   387.0   <2e-16 ***
## PTSdiff     3.259e-02  2.793e-04   116.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.061 on 833 degrees of freedom
## Multiple R-squared:  0.9423, Adjusted R-squared:  0.9423 
## F-statistic: 1.361e+04 on 1 and 833 DF,  p-value: < 2.2e-16

By calculating W = [41(Intercept) + 0.0326(Coef. Est. for PTSdiff)] * PTSdiff

A team would need to have 42 wins for a chance to be in the playoffs PTSdiff <- (42-41)/0.0326

PTSdiff <- (42-41)/0.0326
PTSdiff
## [1] 30.67485

The expected points difference for a team to make it to the postseason is 30.67.