Results

Descriptive Statistics

Descriptive Statistics
  Adverts Sales
Valid 200 200
Missing 0 0
Mean 614.412 193.200
Std. Deviation 485.655 80.699
Minimum 9.104 10.000
Maximum 2271.860 360.000

Scatter Plots

Adverts - Sales

Linear Regression: Single Predictor

Model Summary - Sales
Model R R² Adjusted R² RMSE
M₀ 0.000 0.000 0.000 80.699
M₁ 0.578 0.335 0.331 65.991
Note.  M₁ includes , Adverts
ANOVA
Model   Sum of Squares df Mean Square F p
M₁ Regression 433687.833 1 433687.833 99.587 < .001
  Residual 862264.167 198 4354.870  
  Total 1.296×10+6 199  
Note.  M₁ includes , Adverts
Note.  The intercept model is omitted, as no meaningful information can be shown.
Coefficients
95% CI
Model   Unstandardized Standard Error Standardized t p Lower Upper
M₀ (Intercept) 193.200 5.706 33.857 < .001 181.947 204.453
M₁ (Intercept) 134.140 7.537 17.799 < .001 119.278 149.002
  Adverts 0.096 0.010 0.578 9.979 < .001 0.077 0.115
Bootstrap Coefficients
95% CI*
Model   Unstandardized Bias Standard Error p* Lower Upper
M₀ (Intercept) 193.200 0.085 5.652 < .001 181.951 204.450
M₁ (Intercept) 133.887 -0.115 7.867 < .001 119.379 150.639
  Adverts 0.096 1.358×10-4 0.008 < .001 0.079 0.112
Note.  Bootstrapping based on 5000 replicates.
Note.  Coefficient estimate is based on the median of the bootstrap distribution.
* Bias corrected accelerated.

Q-Q Plot Standardized Residuals

Descriptive Statistics

Descriptive Statistics
  Sales Adverts Airplay Image
Valid 200 200 200 200
Missing 0 0 0 0
Mean 193.200 614.412 27.500 6.770
Std. Deviation 80.699 485.655 12.270 1.395
Minimum 10.000 9.104 0.000 1.000
Maximum 360.000 2271.860 63.000 10.000

Scatter Plots

Sales - Adverts

Sales - Airplay

Sales - Image

Adverts - Airplay

Adverts - Image

Airplay - Image

Correlation

Pearson's Correlations
Variable   Sales Adverts Airplay Image
1. Sales Pearson's r —
p-value —      
2. Adverts Pearson's r 0.578 —
p-value < .001 —    
3. Airplay Pearson's r 0.599 0.102 —
p-value < .001 0.151 —  
4. Image Pearson's r 0.326 0.081 0.182 —
p-value < .001 0.256 0.010 —

Correlation plot

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