• Welcome to the presentation on linear regression analysis using the mtcars dataset.
• Today, we’ll explore how linear regression can help us understand the relationship between car specifications in the mtcars dataset.
• Let’s dive into the world of predictive modeling and uncover insights from this classic dataset.

• The mtcars dataset includes various car specifications.
• Let’s take a look at the first few rows of the dataset:

##                    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

Here is a scatter plot of the car weights vs the miles per gallon per car.

• We’ll formulate a simple linear regression model:

Linear Regression Model: mpg = 37.29 + -5.34 * wt

Model Coefficients: Intercept (Intercept): 37.29 Slope (wt): -5.34

R-squared: 0.7528

Above is the linear regression model for the data comparing car weight to miles per gallon.

There is a moderately negative line of fit to the data. This means that as the weight of the car increase, the miles per gallon the car gets decreases.

Call: lm(formula = mpg ~ wt, data = mtcars)

Residuals: Min 1Q Median 3Q Max -4.5432 -2.3647 -0.1252 1.4096 6.8727

Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.2851 1.8776 19.858 < 2e-16 wt -5.3445 0.5591 -9.559 1.29e-10 — Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ’ ’ 1

Residual standard error: 3.046 on 30 degrees of freedom Multiple R-squared: 0.7528, Adjusted R-squared: 0.7446 F-statistic: 91.38 on 1 and 30 DF, p-value: 1.294e-10

The model’s R-squared value of 0.7528 indicates that approximately 75.28% of the variability in miles per gallon (mpg) can be explained by the weight variable.

##   Weight Predicted_MPG
## 1    2.5      23.92395
## 2    3.0      21.25171
## 3    3.5      18.57948

Predicted miles per gallon (mpg) value based on vehicle weight has practical applications in optimizing vehicle systems, reporting fuel efficiency labels about, and guiding environmental policies These forecasts benefit automotive manufacturers by improving planning for fuel efficiency, helping regulators set standards that about carbon emissions, and empowering consumers to make informed sustainable choices Choosing smarter and more economical ideas helps.

In summary, this study on the mtcars dataset shows that heavier cars tend to have lower fuel efficiency. A math formula was used to understand this relationship: fuel efficiency equals a starting number plus another number multiplied by the car’s weight. The math also tells us that around 75.28% of how fuel-efficient a car is can be explained by its weight. This information is helpful for people buying cars, those who make cars, and those who decide on rules for fuel use. While this is helpful, however, there is still much to explore as far as other factors that affect fuel efficiency.

Thank you for joining the presentation!