##
## Call:
## lm(formula = registered ~ temp + I(temp * temp) + I(temp * temp *
## temp) + season + Promotion + mnth + workingday + weathersit,
## data = bikeshare)
##
## Coefficients:
## (Intercept) temp I(temp * temp)
## 985.1253 -190.0400 20.1688
## I(temp * temp * temp) season2 season3
## -0.4296 613.2094 1023.0692
## season4 Promotion1 mnth2
## 1606.3497 1743.4083 117.2687
## mnth3 mnth4 mnth5
## 127.3456 -75.5088 182.6047
## mnth6 mnth7 mnth8
## 423.6630 292.0030 147.0608
## mnth9 mnth10 mnth11
## 166.2658 -261.3192 -488.0237
## mnth12 workingday weathersit2
## -190.1047 969.3214 -544.4747
## weathersit3
## -2063.0787##
## Call:
## lm(formula = registered ~ temp + I(temp * temp) + I(temp * temp *
## temp) + season + Promotion + mnth + workingday + weathersit,
## data = bikeshare)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3573.3 -273.3 76.2 354.4 1570.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 985.1254 353.8938 2.784 0.00552 **
## temp -190.0400 66.1523 -2.873 0.00419 **
## I(temp * temp) 20.1688 3.5821 5.630 2.59e-08 ***
## I(temp * temp * temp) -0.4296 0.0598 -7.183 1.73e-12 ***
## season2 613.2094 136.1234 4.505 7.77e-06 ***
## season3 1023.0692 162.6551 6.290 5.56e-10 ***
## season4 1606.3497 136.4228 11.775 < 2e-16 ***
## Promotion1 1743.4083 43.8597 39.750 < 2e-16 ***
## mnth2 117.2686 113.2083 1.036 0.30062
## mnth3 127.3456 131.1638 0.971 0.33193
## mnth4 -75.5088 190.5959 -0.396 0.69210
## mnth5 182.6047 204.3843 0.893 0.37193
## mnth6 423.6630 210.3860 2.014 0.04441 *
## mnth7 292.0030 235.9319 1.238 0.21625
## mnth8 147.0608 228.0975 0.645 0.51931
## mnth9 166.2659 205.7132 0.808 0.41922
## mnth10 -261.3192 188.1379 -1.389 0.16528
## mnth11 -488.0237 180.8023 -2.699 0.00712 **
## mnth12 -190.1047 143.7876 -1.322 0.18655
## workingday 969.3214 46.8691 20.681 < 2e-16 ***
## weathersit2 -544.4747 47.2741 -11.517 < 2e-16 ***
## weathersit3 -2063.0787 132.9827 -15.514 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 584.3 on 709 degrees of freedom
## Multiple R-squared: 0.8638, Adjusted R-squared: 0.8598
## F-statistic: 214.1 on 21 and 709 DF, p-value: < 2.2e-16It does not look like there are problems multicollinearity at this time. It appears as though the correlations between variables in this model are low (none outside of -.3 to .3). As for linearity, there may be some issues but the model seems to fit well. The biggest worry for me in terms of linearity was the temperature variable, but setting it to cubic has made me more comfortable with the model.
June (mnth 6) appears to have the most riders. If it were to become unseasonably cold and rainy, this would drop the number of riders by about 544, however it would not change the coefficient for month.
The coefficient for promotion is 1743, meaning there is an average of 1743 additional riders when there is a promotion. This leads me to the initial judgement that the marketing department is correct to an extent, given the fact that Promotions seem to have nearly the biggest impact on number of riders (right behind a bad weather situation).
##
## Call:
## lm(formula = casual ~ temp + I(temp * temp) + I(temp * temp *
## temp) + season + Promotion + mnth + workingday + weathersit,
## data = bikeshare)
##
## Coefficients:
## (Intercept) temp I(temp * temp)
## 990.2946 -130.2807 11.2885
## I(temp * temp * temp) season2 season3
## -0.2195 190.0101 162.0304
## season4 Promotion1 mnth2
## 106.6839 297.9581 7.7147
## mnth3 mnth4 mnth5
## 263.8073 209.7846 203.5973
## mnth6 mnth7 mnth8
## 196.0206 294.5666 170.2349
## mnth9 mnth10 mnth11
## 180.0471 249.6970 110.8257
## mnth12 workingday weathersit2
## 14.3201 -796.4908 -188.9696
## weathersit3
## -569.2973##
## Call:
## lm(formula = casual ~ temp + I(temp * temp) + I(temp * temp *
## temp) + season + Promotion + mnth + workingday + weathersit,
## data = bikeshare)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1292.54 -212.31 -33.07 183.60 1578.29
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 990.29459 217.22571 4.559 6.06e-06 ***
## temp -130.28067 40.60532 -3.208 0.00139 **
## I(temp * temp) 11.28848 2.19876 5.134 3.67e-07 ***
## I(temp * temp * temp) -0.21952 0.03671 -5.980 3.53e-09 ***
## season2 190.01015 83.55474 2.274 0.02326 *
## season3 162.03040 99.84029 1.623 0.10506
## season4 106.68394 83.73849 1.274 0.20308
## Promotion1 297.95811 26.92179 11.068 < 2e-16 ***
## mnth2 7.71469 69.48908 0.111 0.91163
## mnth3 263.80726 80.51047 3.277 0.00110 **
## mnth4 209.78459 116.99079 1.793 0.07337 .
## mnth5 203.59729 125.45433 1.623 0.10506
## mnth6 196.02056 129.13829 1.518 0.12948
## mnth7 294.56663 144.81880 2.034 0.04232 *
## mnth8 170.23493 140.00991 1.216 0.22444
## mnth9 180.04715 126.27007 1.426 0.15434
## mnth10 249.69704 115.48204 2.162 0.03094 *
## mnth11 110.82567 110.97935 0.999 0.31832
## mnth12 14.32013 88.25911 0.162 0.87115
## workingday -796.49078 28.76899 -27.686 < 2e-16 ***
## weathersit2 -188.96961 29.01760 -6.512 1.40e-10 ***
## weathersit3 -569.29732 81.62694 -6.974 7.05e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 358.7 on 709 degrees of freedom
## Multiple R-squared: 0.735, Adjusted R-squared: 0.7272
## F-statistic: 93.64 on 21 and 709 DF, p-value: < 2.2e-16It appears the promotion impacts casual drivers as well, but much less. An average of 297 more casual bikers were riding when there is a promotion, vs.ย an additional 1743 for registered riders. Though far less, causal riders are still influenced significantly by the promotion compared to other variables in the model. The Rsq value is a bit lower, indicating this model is less of a fit for casual riders.
To make a more meaningful report, I need to know the financials information surrounding the bikeshare program. What are the exact business costs for the company? What does the profit margin look like? Without the actually monetary information, it is hard to clean exactly what the promotion is doing. With this information, it would be much more clear as to weather or not the promotion was a success both for registered and casual bikers.