> Dataset$isOwn <- with(Dataset, ifelse(OwnHome=="Own", 1, 0))> Dataset$isRent <- with(Dataset, ifelse(OwnHome=="Rent", 1, 0))> Dataset$isMale <- with(Dataset, ifelse(Children=="Male", 1, 0))> Dataset$isFemale <- with(Dataset, ifelse(Children=="Female", 1, 0))> Dataset$isSingle <- with(Dataset, ifelse(Married=="Single", 1, 0))> Dataset$isMarried <- with(Dataset, ifelse(Married=="Married", 1, 0))> Dataset$isFar <- with(Dataset, ifelse(Location=="Far", 1, 0))> Dataset$isClose <- with(Dataset, ifelse(Location=="Close", 1, 0))> Dataset$isHigh <- with(Dataset, ifelse(History=="High", 1, 0))> Dataset$isMedium <- with(Dataset, ifelse(History=="Medium", 1, 0))> Dataset$isLow <- with(Dataset, ifelse(History=="Low", 1, 0))> Dataset$isMale <- with(Dataset, ifelse(Gender=="Male", 1, 0))> Dataset$isFemale <- with(Dataset, ifelse(Gender=="Female", 1, 0))> RegModel.2 <-
+ lm(AmountSpent~Catalogs+Children+isClose+isFemale+isHigh+isLow+isMarried+isOwn+Salary,
+
+ data=Dataset)> summary(RegModel.2)
Call:
lm(formula = AmountSpent ~ Catalogs + Children + isClose + isFemale +
isHigh + isLow + isMarried + isOwn + Salary, data = Dataset)
Residuals:
Min 1Q Median 3Q Max
-1573.90 -285.08 -22.51 217.67 2808.80
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.818e+01 7.910e+01 0.356 0.7217
Catalogs 4.032e+01 2.865e+00 14.074 < 2e-16 ***
Children -2.758e+02 2.279e+01 -12.098 < 2e-16 ***
isClose -6.135e+02 4.386e+01 -13.987 < 2e-16 ***
isFemale 5.322e+01 3.732e+01 1.426 0.1544
isHigh 3.460e+02 5.989e+01 5.778 1.15e-08 ***
isLow 1.014e+02 5.669e+01 1.789 0.0741 .
isMarried 2.162e+00 4.713e+01 0.046 0.9634
isOwn 9.905e+00 3.970e+01 0.249 0.8031
Salary 1.819e-02 1.175e-03 15.489 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 463.6 on 687 degrees of freedom
(303 observations deleted due to missingness)
Multiple R-squared: 0.788, Adjusted R-squared: 0.7852
F-statistic: 283.7 on 9 and 687 DF, p-value: < 2.2e-16When looking at the summary of my linear regression model, the adjusted R-squared value is 0.785 which means there is a strong correlation between the variables I made. isClose and isHigh are two of the created variables that are significant at the 0.001 level.
> confint(RegModel.2) 2.5 % 97.5 %
(Intercept) -127.12521232 183.49086621
Catalogs 34.69914725 45.94993230
Children -320.50314986 -230.99709491
isClose -699.63959359 -527.39679481
isFemale -20.06243251 126.50306496
isHigh 228.43758981 463.61855322
isLow -9.90229766 212.70533984
isMarried -90.38145469 94.70493996
isOwn -68.04717645 87.85781842
Salary 0.01588792 0.02050067When looking at the confidence intervals, there is a possibility of 0 being between the variables on each side of the distribution. For this reason, we fail to reject the null hypothesis.
> RegModel.3 <-
+ lm(AmountSpent~Catalogs+Children+isFar+isMale+isMedium+isRent+isSingle+Salary,
+ data=Dataset)
> summary(RegModel.3)
Call:
lm(formula = AmountSpent ~ Catalogs + Children + isFar + isMale +
isMedium + isRent + isSingle + Salary, data = Dataset)
Residuals:
Min 1Q Median 3Q Max
-1716.7 -293.6 -20.7 219.1 2708.0
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.203e+02 8.474e+01 -4.959 8.92e-07 ***
Catalogs 4.187e+01 2.825e+00 14.821 < 2e-16 ***
Children -3.176e+02 1.733e+01 -18.322 < 2e-16 ***
isFar 6.676e+02 3.960e+01 16.857 < 2e-16 ***
isMale -4.757e+01 3.746e+01 -1.270 0.205
isMedium -2.177e+02 3.885e+01 -5.604 3.03e-08 ***
isRent -1.792e+01 3.980e+01 -0.450 0.653
isSingle -8.260e+00 4.732e+01 -0.175 0.861
Salary 2.041e-02 8.737e-04 23.359 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 465.9 on 688 degrees of freedom
(303 observations deleted due to missingness)
Multiple R-squared: 0.7856, Adjusted R-squared: 0.7831
F-statistic: 315.1 on 8 and 688 DF, p-value: < 2.2e-16When creating another linear regression model using the variables that were not used in the first regression model, isMedium and isFar are significant at the 0.001 level. This means that Location factor variable and History factor variable are good estimators of Amount Spent. Even in the last regression model, their counterparts isHigh and isClose were both significant.
> confint(RegModel.3) 2.5 % 97.5 %
(Intercept) -586.63721685 -253.87164463
Catalogs 36.32747340 47.42193770
Children -351.58551898 -283.52475709
isFar 589.80119513 745.31291430
isMale -121.10582331 25.97413722
isMedium -293.99004593 -141.43269985
isRent -96.05303636 60.22209089
isSingle -101.16478327 84.64479777
Salary 0.01869461 0.02212564Again, when looking at the confidence intervals, there is a possibility of 0 being between the variables on each side of the distribution. For this reason, we fail to reject the null hypothesis.