Linear regression (lm) in R Programming - Step-by-Step Execution

Concept Flow - Linear regression (lm)

Start with data

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Choose dependent and independent variables

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Fit linear model lm(y ~ x)

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Calculate coefficients (intercept, slope)

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Use model to predict y from x

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Evaluate model fit (summary)

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End

Linear regression fits a straight line to data by finding coefficients that best predict y from x.

Execution Sample

R Programming

x <- c(1, 2, 3, 4, 5)
y <- c(2, 4, 5, 4, 5)
model <- lm(y ~ x)
summary(model)

Fit a linear model predicting y from x and show the summary of the fit.

Execution Table

Step	Action	Evaluation	Result
1	Create vector x	x = c(1,2,3,4,5)	x = 1,2,3,4,5
2	Create vector y	y = c(2,4,5,4,5)	y = 2,4,5,4,5
3	Fit model lm(y ~ x)	Calculate coefficients	model with intercept and slope
4	Extract coefficients	coef(model)	Intercept ≈ 2.2, Slope ≈ 0.6
5	Predict y for x=3	predict(model, newdata=data.frame(x=3))	Predicted y ≈ 3.8
6	Show summary(model)	summary(model)	R-squared ≈ 0.6, p-values, residuals
7	End	Model fit complete	Ready for predictions or diagnostics

💡 All steps complete, model fitted and summary available

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
x	NULL	[1,2,3,4,5]	[1,2,3,4,5]	[1,2,3,4,5]	[1,2,3,4,5]	[1,2,3,4,5]
y	NULL	NULL	[2,4,5,4,5]	[2,4,5,4,5]	[2,4,5,4,5]	[2,4,5,4,5]
model	NULL	NULL	NULL	lm object	lm object	lm object
coefficients	NULL	NULL	NULL	NULL	Intercept=2.2, Slope=0.6	Intercept=2.2, Slope=0.6

Key Moments - 3 Insights

Why does the model have an intercept and slope?

The intercept and slope come from fitting the line y = intercept + slope * x that best matches the data (see execution_table step 4).

What does the summary(model) tell us?

It shows how well the line fits the data, including R-squared and p-values (see execution_table step 6).

Why do we use predict() after fitting the model?

predict() uses the fitted line to estimate y for new x values (see execution_table step 5).

Visual Quiz - 3 Questions

Look at the execution table, what is the approximate slope coefficient after fitting the model?

A 4.0

B 2.2

C 0.6

D 5.0

💡 Hint

Check the 'Extract coefficients' row in the execution_table where coefficients are shown.

At which step do we get the model object created?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look for the step where lm(y ~ x) is called and the model is fitted.

If we add a new x value 6 and predict y, which step would this action be similar to?

A Step 5

B Step 1

C Step 3

D Step 6

💡 Hint

Prediction of y for a new x value is done in the step where predict() is used.

Concept Snapshot

Linear regression fits a line y = intercept + slope * x
Use lm(y ~ x) in R to fit the model
Coefficients show intercept and slope
summary(model) shows fit quality
predict(model, newdata) estimates y for new x

Full Transcript

This visual execution traces fitting a linear regression model in R using lm(). We start by creating numeric vectors x and y. Then we fit the model lm(y ~ x), which calculates the best intercept and slope to predict y from x. The coefficients are extracted and show the intercept around 2.2 and slope around 0.6. Using predict(), we estimate y for a new x value. Finally, summary(model) gives statistics about the fit quality like R-squared. Variables x, y, model, and coefficients change as we progress through these steps.