Suppose that you want to build a regression model that predicts the price of cars using a data set named cars.

Q1. Per the scatter plot and the computed correlation coefficient, describe relationships between the two variables - price and weight.

Make sure to interpret the direction and the magnitude of the relationship. In addition, keep in mind that correlation (or regression) coefficients do not show causation but only association.

There is strong positive correlation between the price and weight of the cars. The cars that are ligter are cheaper, and cars that are heavier are more expensive, like sedans compared to trucks.

Create scatterplots

## 'data.frame':    54 obs. of  6 variables:
##  $ type      : Factor w/ 3 levels "large","midsize",..: 3 2 2 2 2 1 1 2 1 2 ...
##  $ price     : num  15.9 33.9 37.7 30 15.7 20.8 23.7 26.3 34.7 40.1 ...
##  $ mpgCity   : int  25 18 19 22 22 19 16 19 16 16 ...
##  $ driveTrain: Factor w/ 3 levels "4WD","front",..: 2 2 2 3 2 2 3 2 2 2 ...
##  $ passengers: int  5 5 6 4 6 6 6 5 6 5 ...
##  $ weight    : int  2705 3560 3405 3640 2880 3470 4105 3495 3620 3935 ...

## [1] 0.758112

Interpretation

Run a regression model for price with one explanatory variable, weight, and answer Q2 through Q5.

Q2. Is the coefficient of weight statistically significant at 5%? Interpret the coefficient.

Yes. It is significant at 5%.

Q3. What price does the model predict for a car that weighs 4000 pounds?

Hint: Check the units of the variables in the openintro manual.

The line of regression shows that the average 4000lb car would cost approx. $32,000, but the only peice of data in the 4000lb range shows that it was purchased at around $48,000

Q4. What is the reported residual standard error? What does it mean?

The reported residual standard error is 7.575 on 52 degrees of freedom. This basically shows us how accurate the line of best fit is that cuts through the data.

Q5. What is the reported adjusted R squared? What does it mean?

The reported adjusted R squared is 0.5666 which translates to 56.6%. This shows the variabillity in terms of price as a dependant variable and weightvbeing the independant variable.

Run a second regression model for price with two explanatory variables: weight and passengers, and answer Q6.

Q6. Which of the two models better fits the data? Discuss your answer by comparing the residual standard error and the adjusted R squared between the two models.

The second model fits the model better because it hasa a smaller residual error, and a larger adjusted R squared meaning it is more accurate.

Build regression model

## 
## Call:
## lm(formula = price ~ weight, data = cars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -12.767  -3.766  -1.155   2.568  35.440 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -20.295205   4.915159  -4.129 0.000132 ***
## weight        0.013264   0.001582   8.383 3.17e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.575 on 52 degrees of freedom
## Multiple R-squared:  0.5747, Adjusted R-squared:  0.5666 
## F-statistic: 70.28 on 1 and 52 DF,  p-value: 3.173e-11
## 
## Call:
## lm(formula = price ~ weight + passengers, data = cars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.647  -3.688  -1.134   2.677  33.704 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -7.348709   7.480301  -0.982   0.3305    
## weight       0.015891   0.001925   8.256  5.8e-11 ***
## passengers  -4.094465   1.831085  -2.236   0.0297 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.3 on 51 degrees of freedom
## Multiple R-squared:  0.6127, Adjusted R-squared:  0.5975 
## F-statistic: 40.34 on 2 and 51 DF,  p-value: 3.127e-11

Interpretation