mult linear regression heart

Make sure the data meets all the 4 assumptions for Linear Regression Perform the linear regression analysis Check for homoscedasticity Visualize the results with graphs Report the results

summary(model)

Call:
lm(formula = heart.disease ~ biking + smoking, data = heart_Lab5)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.1789 -0.4463  0.0362  0.4422  1.9331 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 14.984658   0.080137  186.99   <2e-16 ***
biking      -0.200133   0.001366 -146.53   <2e-16 ***
smoking      0.178334   0.003539   50.39   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.654 on 495 degrees of freedom
Multiple R-squared:  0.9796,    Adjusted R-squared:  0.9795 
F-statistic: 1.19e+04 on 2 and 495 DF,  p-value: < 2.2e-16

Assumption 1: linearity

For biking plotted with heart disease, we see clearly that they are linearly related

From the plot of smoking vs heart disesase the linearity is much less apparent but still visably linear

Assumption 2: Independence independence can be confirmed by checking if the residuals are randomly scattered around the horizontal line at zero which they are when plotted with our observations

plot(model$residuals, xlab = "Observation number", ylab = "Residuals")
abline(h = 0)

Assumption 3: Homoscedasticity We see randomness/evenness when plotting the residuals and predicted values of our model suggesting Homoscedasticity

plot(model$fitted.values, model$residuals, main = "Residuals vs. Fitted values plot", xlab = "Fitted values", ylab = "Residuals")
abline(h = 0)

Assumption 4: Normality

from the qq plot we see normality from the plot of the residuals due to residuals plotted against theoretical normal distributed residuals

hist(model$residuals, main = "Histogram of residuals")

qqnorm(model$residuals)
qqline(model$residuals)

Significance between predictor variables and heart disease p<2e-16

summary(model)

Call:
lm(formula = heart.disease ~ biking + smoking, data = heart_Lab5)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.1789 -0.4463  0.0362  0.4422  1.9331 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 14.984658   0.080137  186.99   <2e-16 ***
biking      -0.200133   0.001366 -146.53   <2e-16 ***
smoking      0.178334   0.003539   50.39   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.654 on 495 degrees of freedom
Multiple R-squared:  0.9796,    Adjusted R-squared:  0.9795 
F-statistic: 1.19e+04 on 2 and 495 DF,  p-value: < 2.2e-16

The adjusted R-squared value of 0.9795 suggests that the model explains a large proportion of the variability in the response variable. Therefore, we can conclude that both biking and smoking have a significant effect on heart disease in the sample of 500 towns. The coefficients of the model are significant at the 0.001 level, and the p-value for the overall F-statistic is <2.2e-16, which means that the model as a whole is statistically significant. we can conclude that both biking and smoking have a significant effect on heart disease in the sample of 500 town