Exercise 11

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Linear Regression

The steps to create the relationship is −

• Carry out the experiment of gathering a sample of observed values of height and corresponding weight.

• Create a relationship model using the lm() functions in R.

• Find the coefficients from the model created and create the mathematical equation using these

• Get a summary of the relationship model to know the average error in prediction. Also called residuals.

• To predict the weight of new persons, use the predict() function in R.

Create Relationship Model

# The predictor variable
x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)

# The response variable
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)

# Apply the lm() function.
relation <- lm(y~x)
relation

## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##    -38.4551       0.6746

Get the Summary of the Relationship

summary(relation)

## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.3002 -1.6629  0.0412  1.8944  3.9775 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -38.45509    8.04901  -4.778  0.00139 ** 
## x             0.67461    0.05191  12.997 1.16e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.253 on 8 degrees of freedom
## Multiple R-squared:  0.9548, Adjusted R-squared:  0.9491 
## F-statistic: 168.9 on 1 and 8 DF,  p-value: 1.164e-06

Predict

# Find y for an x of 170.
a <- data.frame(x=170)
result <- predict(relation,a)
result

##        1 
## 76.22869

Plots

# Plot the chart.
plot(x,y,
     col = "blue",
     main = "Linear Regression",
     abline(lm(y~x)),
     cex = 1.3,pch = 16)

plot(lm(y~x))