Scottish Hill Climb racesWe want to predict the record time for women in a Scottish Hill Climb race. Thereare two x variables to choose from, Distance and Climb. Here are the first few rowsfrom the data table.RaceMen (mins)Women(mins) Distance(km) Climb (m)Alva Games Hill Race18.65025.8172.5385Aonach Mor Uphill Race22.25026.4674.0610Arrochar Alps187.650249.43325.02400Once you have chosen the best single x variable to predict the record time forwomen, does it help to add the 2nd x variable?Here is the information for the two single x variables.Coefficients for Distance:TermCoef SE CoefT-ValueP-ValueConstant-7.15 3.32-2.160.034Distance(km) 6.765 0.24627.550.000Model Summary for Distance:R-sqR-sq(adj)R-sq(pred)17.822289.72%89.60%88.19%Coefficients for Climb:TermCoefSE CoefT-Value P-ValueConstant2.604.200.62 0.538 Climb (m)0.097170.0049719.55 0.000Model Summary for Climb:R-sqR-sq(adj)R-sq(pred)23.930181.46%81.25%80.54%Here is the information for the 3 dimensional relationship between x1, x2, and Y.Multiple Linear Relationship for the women:Coefficients:TermCoefSE CoefT-Value P-ValueConstant-11.701.91-6.110.000Distance(km)4.4320.22220.010.000Climb (m)0.045260.0033413.560.000Model Summary:SR-sqR-sq(adj)R-sq(pred)10.120896.72%96.65%96.09%Does it help to add the second x variable in this case?O YesO You can't tell from this informationO No

The regression model would be more accurate as R - sq value getting higher side. The R - sq value of any regression model interprets, how much % variation in dependent variable explained by the overall model. Let's Variable X1 = Distance Variable X2 = Climb Variable Y = record time for women Simply, the model with higher R- sq value would be more accurate. From the given outputs , Model 1 : R-sq value for Variable Distance is 89.72% and it interprets that approximately 89.72% of the variation in record time for women is explained by the Distance (Km) Model 2 :As well as R - sq value for variable Climb is 81.46% and it interprets that approximately 81.46% of the variation in record time for women is explained by the Climb (m). Model 2 :After performing the multiple regression model, by combining the variables X1 = Distance & X2 = Climb. The R - sq value for the new model is significantly improved as 96.72%. It tells that total 96.72% of the variation the record time for women is explained by the overall model. Further, it defines that total 96.72% of the considered data explains the estimated regression model is good fit fit. Conclusion : From the three regression models, the R- sq value (96.72) is higher for combined regression model as compared to other two individual models. Therefore, adding the second x variable obviously helps for improvement of model in this case. Hence yes, adding the second variable helps in this case.