library(tidyverse)
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library(readxl)
data(mtcars)
dependent <- "mpg"
independent_vars <- c("hp", "wt")
model <- lm(mpg ~ hp + wt, data = mtcars)
summary(model)
## 
## Call:
## lm(formula = mpg ~ hp + wt, data = mtcars)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.941 -1.600 -0.182  1.050  5.854 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 37.22727    1.59879  23.285  < 2e-16 ***
## hp          -0.03177    0.00903  -3.519  0.00145 ** 
## wt          -3.87783    0.63273  -6.129 1.12e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.593 on 29 degrees of freedom
## Multiple R-squared:  0.8268, Adjusted R-squared:  0.8148 
## F-statistic: 69.21 on 2 and 29 DF,  p-value: 9.109e-12

The R-squared is 0.83, so about 83% of the variation in mpg is explained by horsepower and weight. Both hp and wt have p-values under 0.05, so they are statistically significant.

The estimate for wt is -3.88, meaning that as weight increases, mpg goes down. Heavier cars use more gas.

plot(model, which=1)

The Residuals vs Fitted plot shows a slight curve, which suggests the model does not perfectly meet the assumption of linearity. However, the pattern is minor, so the model still gives a useful estimate.