*41*

The **method of least squares** is a method we can use to find the regression line that best fits a given dataset.

The following video provides a brief explanation of this method:

To use the method of least squares to fit a regression line in R, we can use the **lm()** function.

This function uses the following basic syntax:

model

The following example shows how to use this function in R.

**Example: Method of Least Squares in R**

Suppose we have the following data frame in R that shows the number of hours studied and the corresponding exam score for 15 students in some class:

#create data frame df frame(hours=c(1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14), score=c(64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89)) #view first six rows of data frame head(df) hours score 1 1 64 2 2 66 3 4 76 4 5 73 5 5 74 6 6 81

We can use the **lm()** function to use the method of least squares to fit a regression line to this data:

#use method of least squares to fit regression line model #view regression model summary summary(model) Call: lm(formula = score ~ hours, data = df) Residuals: Min 1Q Median 3Q Max -5.140 -3.219 -1.193 2.816 5.772 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 65.334 2.106 31.023 1.41e-13 *** hours 1.982 0.248 7.995 2.25e-06 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 3.641 on 13 degrees of freedom Multiple R-squared: 0.831, Adjusted R-squared: 0.818 F-statistic: 63.91 on 1 and 13 DF, p-value: 2.253e-06

From the values in the **Estimate** column of the output,Â we can write the following fitted regression line:

Exam Score = 65.334 + 1.982(Hours)

Hereâ€™s how to interpret each coefficient in the model:

**Intercept**: For a student who studies 0 hours, the expected exam score is**65.334**.**hours**: For each additional hour studied, the expected exam score increases by**1.982**.

We can use this equation to estimate the exam score a student will receive based on their hours studied.

For example, if a student studies for 5 hours, we would estimate that their exam score would be 75.244:

Exam Score = 65.334 + 1.982(5) = 75.244

Lastly, we can create a scatter plot of the original data with the fitted regression line overlaid on the plot:

#create scatter plot of data plot(df$hours, df$score, pch=16, col='steelblue') #add fitted regression line to scatter plot abline(model)

The blue circles represent the data and the black line represents the fitted regression line.

**Additional Resources**

The following tutorials explain how to perform other common tasks in R:

How to Create a Residual Plot in R

How to Test for Multicollinearity in R

How to Perform Curve Fitting in R