Data

The data in the LoveAndMoney.TXT file was collected by Shonda Kuiper. The variable Money represents the amount the individual spent last Valentine’s Day. The variable Love is a score on a satisfaction scale.

  LoveMoney <- read.csv("LoveandMoney.csv")
  head(LoveMoney)  
##   X Love MoneySpent
## 1 1    0       25.0
## 2 2  100      275.0
## 3 3    0       26.0
## 4 4    0       27.0
## 5 5    2       33.0
## 6 6    5       41.5

Univariate Statistics

Plots and numeric descriptives of the individual variables are not particularly remarkable.

  p_load(mosaic)
  bwplot(~MoneySpent, data=LoveMoney)

  bwplot(~Love, data=LoveMoney)

  histogram(~MoneySpent, data=LoveMoney)

  histogram(~Love, data=LoveMoney)

Bivariate Analysis

A scatterplot of MoneySpent as a function of Love indicates that there may be a linear relationship between the two variables.

  xyplot(MoneySpent~Love,LoveMoney,pch=16,cex=1.5)

We fit the linear model.

  LoveMoney.lm.l=lm(MoneySpent~Love,data=LoveMoney)
  summary(LoveMoney.lm.l)
## 
## Call:
## lm(formula = MoneySpent ~ Love, data = LoveMoney)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.9567 -2.9595  0.5433  3.2689  4.0476 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 25.94950    1.08919   23.82   <2e-16 ***
## Love         2.50014    0.01761  141.99   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.512 on 28 degrees of freedom
## Multiple R-squared:  0.9986, Adjusted R-squared:  0.9986 
## F-statistic: 2.016e+04 on 1 and 28 DF,  p-value: < 2.2e-16

The resultant model supports the strong relationship that was seen in the scatterplot. We follow the fitting of the linear model with a quick look at the residuals.

  xyplot(LoveMoney.lm.l$resid~LoveMoney$Love,col="red",pch=16,cex=2)

  plot(LoveMoney.lm.l)

Just a little reminder that the patterns hidden within “linear” relationships are not always linear.