Question

Team	Pts./Game	Number of Wins
Charlotte	108.2	36
Minnesota	109.5	47
Houston	112.4	65
LA Clippers	109	42
Cleveland	110.9	50
Milwaukee	106.5	44
Phoenix	103.9	21
Philadelphia	109.8	52
Toronto	111.7	59
Brooklyn	106.6	28
Okla City	107.9	48
Denver	110	46
Washington	106.6	43
Utah	104.1	48
LA Lakers	108.1	35
Golden State	113.5	58
Memphis	99.3	22
Portland	105.6	49
Boston	104	55
San Antonio	102.7	47
New Orleans	111.7	48
Atlanta	103.4	24
Orlando	103.4	25
Miami	103.4	44
New York	104.5	29
Indiana	105.6	48
Detroit	103.8	39
Chicago	102.9	27
Dallas	102.3	24
Sacramento	98.8	27

Use your numerical and/or graphical output:

1. Explain the linearity & equal spread conditions/assumptions for this dataset. Include the appropriate graphs from your output to support your answer.
2. Explain graphically and numerically the strength & direction between the explanatory/response variables & outliers. Include the appropriate graphs from your output to support your answer.

Regression output: Include the appropriate graphs from your output to support your answers.

3. Report the regression equation. Interpret the slope and y-intercept. Give an example of a residual from this linear regression model. Explain the importance of residuals to linear regression.
4. Report and discuss the predictions (# of wins) for two teams, Team A and Team B, whose projected points in a game are 106 and 96.2, respectively.
5. Report and interpret the correlation coefficient, coefficient of determination, and information about lurking variables.

Answer 1

The graph showing relationship between Pts/Game and No. of wins is:

The variables seem positively linearly correlated from the chart above as increase in pts/game leads to increase in No. of wins. The scatter plot also shows the data spread around roighly around a central line, hence the equality of variance assumption for regression modeling is satisfied.

Correlation between explanatory and response variables, r = 0.704. Hence the response variable (No. of wins) and explanatory variable (Pts/Game) are moderately linearly correlated.

Carrying out regression in Excel (go to Data tab->Data analysis->Regression and choose Pts/Game as X-axis and No. of wins as Y-axis), we get the following output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.703544
R Square	0.494975
Adjusted R Square	0.476938
Standard Error	8.839378
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2144.231	2144.230946	27.44278075	1.44485E-05
Residual	28	2187.769	78.13460908
Total	29	4332
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-199.568	45.95067	-4.343092683	0.000166464	-293.6937043	-105.4423399
Pts./Game	2.262324	0.431858	5.238585758	1.44485E-05	1.377703612	3.146944934

The regression equation obtained is: No. of Wins = -199.57 + 2.262 * Pts/Game

The intercept of -199.57 tells that for Pts/Game = 0, No. of Wins = -199.568 ~ -200 (which means lots of losses).

The slope of 2.262 tells that for per unit increase in Pts/Game, No. of Wins increases by 2.262

Prediction for Team A:  No. of Wins = -199.57 + 2.262 * 106 ~ 40

Prediction for Team B: No. of Wins = -199.57 + 2.262 * 96.2 ~ 18

Correlation coefficient, r = 0.704,

Coefficient of determination, r² = 0.495

The lurking variable here can be number of games played, which is not included as an explanatory variable, and might have an impact on the response variable No. of wins.