project_regression

Project

Author: Sulaiman Allouh

Date: 23/Oct/2024

{Exploratory Data Analysis} data(mtcars) head(mtcars) summary(mtcars)

                   mpg cyl disp  hp drat    wt  qsec vs am gear carb Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4 Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4 Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1 Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1 Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2 Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

      mpg             cyl             disp             hp             drat             wt             qsec        Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0   Min.   :2.760   Min.   :1.513   Min.   :14.50    1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5   1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89    Median :19.20   Median :6.000   Median :196.3   Median :123.0   Median :3.695   Median :3.325   Median :17.71    Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7   Mean   :3.597   Mean   :3.217   Mean   :17.85    3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0   3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90    Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0   Max.   :4.930   Max.   :5.424   Max.   :22.90          vs               am              gear            carb        Min.   :0.0000   Min.   :0.0000   Min.   :3.000   Min.   :1.000    1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000    Median :0.0000   Median :0.0000   Median :4.000   Median :2.000    Mean   :0.4375   Mean   :0.4062   Mean   :3.688   Mean   :2.812    3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000    Max.   :1.0000   Max.   :1.0000   Max.   :5.000   Max.   :8.000

```{Visualize the data} library(ggplot2) ggplot(mtcars, aes(x = factor(am), y = mpg)) + geom_boxplot() + labs(x = “Transmission (0 = Automatic, 1 = Manual)”, y = “MPG”, title = “MPG by Transmission Type”)


![](images/clipboard-1736740353.png)

```{Fit a simple linear model}
model1 <- lm(mpg ~ factor(am), data = mtcars)
summary(model1)

Residuals:     Min      1Q  Median      3Q     Max  -9.3923 -3.0923 -0.2974  3.2439  9.5077   Coefficients:             Estimate Std. Error t value Pr(>|t|)     (Intercept)   17.147      1.125  15.247 1.13e-15 *** factor(am)1    7.245      1.764   4.106 0.000285 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Residual standard error: 4.902 on 30 degrees of freedom Multiple R-squared:  0.3598, Adjusted R-squared:  0.3385  F-statistic: 16.86 on 1 and 30 DF,  p-value: 0.000285

{Fit a simple linear model} model2 <- lm(mpg ~ factor(am) + wt + hp + qsec, data = mtcars) summary(model2)

Residuals:     Min      1Q  Median      3Q     Max  -3.4975 -1.5902 -0.1122  1.1795  4.5404   Coefficients:             Estimate Std. Error t value Pr(>|t|)    (Intercept) 17.44019    9.31887   1.871  0.07215 .  factor(am)1  2.92550    1.39715   2.094  0.04579 *  wt          -3.23810    0.88990  -3.639  0.00114 ** hp          -0.01765    0.01415  -1.247  0.22309    qsec         0.81060    0.43887   1.847  0.07573 .  --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Residual standard error: 2.435 on 27 degrees of freedom Multiple R-squared:  0.8579,    Adjusted R-squared:  0.8368  F-statistic: 40.74 on 4 and 27 DF,  p-value: 4.589e-11