Results

Linear Regression: Multiple Predictors

Model Summary - Sales
Model		R		R²		Adjusted R²		RMSE		AIC		BIC		R² Change		F Change		df1		df2		p
M₀		0.000		0.000		0.000		80.699		2326.863		2333.460		0.000				0		199
M₁		0.815		0.665		0.660		47.087		2114.337		2130.828		0.665		129.498		3		196		< .001

Note. M₁ includes Adverts, Airplay, Image

ANOVA
Model				Sum of Squares		df		Mean Square		F		p
M₁		Regression		861377.418		3		287125.806		129.498		< .001
		Residual		434574.582		196		2217.217
		Total		1.296×10⁺⁶		199

Note. M₁ includes Adverts, Airplay, Image
Note. The intercept model is omitted, as no meaningful information can be shown.

Coefficients
														95% CI				Collinearity Statistics
Model				Unstandardized		Standard Error		Standardized		t		p		Lower		Upper		Tolerance		VIF
M₀		(Intercept)		193.200		5.706				33.857		< .001		181.947		204.453
M₁		(Intercept)		-26.613		17.350				-1.534		0.127		-60.830		7.604
		Adverts		0.085		0.007		0.511		12.261		< .001		0.071		0.099		0.986		1.015
		Airplay		3.367		0.278		0.512		12.123		< .001		2.820		3.915		0.959		1.043
		Image		11.086		2.438		0.192		4.548		< .001		6.279		15.894		0.963		1.038

Bootstrap Coefficients
												95% CI*
Model				Unstandardized		Bias		Standard Error		p*		Lower		Upper
M₀		(Intercept)		193.200		0.081		5.711		< .001		182.199		204.600
M₁		(Intercept)		-26.362		0.766		15.983		0.108		-55.858		5.846
		Adverts		0.085		-9.542×10^-5		0.007		< .001		0.071		0.098
		Airplay		3.359		-0.001		0.309		< .001		2.771		3.987
		Image		11.091		-0.099		2.247		< .001		6.477		15.298

Note. Bootstrapping based on 5000 replicates.
Note. Coefficient estimate is based on the median of the bootstrap distribution.
* Bias corrected accelerated.

Descriptives
		N		Mean		SD		SE
Sales		200		193.200		80.699		5.706
Adverts		200		614.412		485.655		34.341
Airplay		200		27.500		12.270		0.868
Image		200		6.770		1.395		0.099

Part And Partial Correlations
Model				Partial		Part
M₁		Adverts		0.659		0.507
		Airplay		0.655		0.501
		Image		0.309		0.188

Note. The intercept model is omitted, as no meaningful information can be shown.

Collinearity Diagnostics
								Variance Proportions
Model		Dimension		Eigenvalue		Condition Index		(Intercept)		Adverts		Airplay		Image
M₁		1		3.562		1.000		0.003		0.023		0.011		0.003
		2		0.308		3.401		0.006		0.960		0.053		0.008
		3		0.109		5.704		0.054		0.015		0.932		0.069
		4		0.020		13.219		0.937		0.002		0.003		0.921

Note. The intercept model is omitted, as no meaningful information can be shown.

Influential Cases
Case Number		Std. Residual		Sales		Predicted Value		Residual		Cook's Distance		DFBETAS:Intercept		DFBETAS:Adverts		DFBETAS:Airplay		DFBETAS:Image		Covariance Ratio
1		2.177		330.000		229.920		100.080		0.059		-0.316		-0.242		0.158		0.353		0.971
2		-2.323		120.000		228.949		-108.949		0.011		0.013		-0.126		0.009		-0.019		0.920	*
10		2.130		300.000		200.466		99.534		0.018		-0.013		-0.156		0.168		0.007		0.944
47		-2.461		40.000		154.970		-114.970		0.024		0.066		0.196		0.048		-0.179		0.915	*
52		2.099		190.000		92.597		97.403		0.033		0.353		-0.029		-0.137		-0.270		0.960
55		-2.456		190.000		304.123		-114.123		0.040		0.174		-0.326		-0.023		-0.124		0.925	*
61		2.104		300.000		201.190		98.810		0.006		8.189×10^-4		-0.015		0.028		0.021		0.937	*
68		-2.364		70.000		180.416		-110.416		0.022		-0.003		0.211		-0.148		-0.018		0.924	*
100		2.095		250.000		152.713		97.287		0.031		0.061		0.145		-0.300		0.068		0.959
164		-2.629		120.000		241.324		-121.324		0.071		0.180		0.290		-0.401		-0.117		0.920	*
169		3.093		360.000		215.868		144.132		0.051		-0.168		-0.258		0.257		0.170		0.853	*
200		-2.088		110.000		207.206		-97.206		0.025		0.166		-0.046		0.142		-0.259		0.954

* Potentially influential case, according to the selected influence measure.

Residuals vs. Predicted

Standardized Residuals Histogram

Q-Q Plot Standardized Residuals

Partial Regression Plots

Sales vs. Adverts

Sales vs. Airplay

Sales vs. Image