Problem:

Using the “cars” dataset in R, build a linear model for stopping distance as a function of speed and replicate the analysis of your textbook chapter 3 (visualization, quality evaluation of the model, and residual analysis.)

## Structure of Daataset: cars
## 'data.frame':    50 obs. of  2 variables:
##  $ speed: num  4 4 7 7 8 9 10 10 10 11 ...
##  $ dist : num  2 10 4 22 16 10 18 26 34 17 ...
## 
## Summary of cars
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00
## 
## We can see that there is a record showing maximum speed of 25 for a stopping distance of 120
## `geom_smooth()` using formula 'y ~ x'

## 
## There is definitely a linear pattern between stopping distance and speed.
## 
## Linear Model Parameters
## 
## Call:
## lm(formula = dist ~ speed, data = cars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.5791     6.7584  -2.601   0.0123 *  
## speed         3.9324     0.4155   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
## F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12
## 
## The equation of the linear model is : Stopping distance= 3.9324*speed -17.5791, b or y-intercept = -17.5791, slope or a-coeficient = 3.9324, there is normally an error since the linear model isn;t 100% fit.
## 
## Linear Model Validation
## 
## Nearly Normal Residuals

## 
## The following function calls produce the residuals plot for our model.

## 
## The Q-Q plot provides a nice visual indication of whether the residuals from the model are normally distributed.

## 
## There are some outliers in the data but the linear model is validated as error aren't significant