# 27.1: Linear Regression (Section 26.1)

- Page ID
- 8858

To perform linear regression in R, we use the `lm()`

function. Let’s generate some data and use this function to compute the linear regression solution.

```
npoints <- 100
intercept = 10
# slope of X/Y relationship
slope=0.5
# this lets us control the strength of the relationship
# by varying the amount of noise added to the y variable
noise_sd = 0.6
regression_data <- tibble(x = rnorm(npoints)) %>%
mutate(y = x*slope + rnorm(npoints)*noise_sd + intercept)
ggplot(regression_data,aes(x,y)) +
geom_point()
```

We can then apply `lm()`

to these data:

```
lm_result <- lm(y ~ x, data=regression_data)
summary(lm_result)
```

```
##
## Call:
## lm(formula = y ~ x, data = regression_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5563 -0.3042 -0.0059 0.3804 1.2522
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.9761 0.0580 172.12 < 2e-16 ***
## x 0.3725 0.0586 6.35 6.6e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.58 on 98 degrees of freedom
## Multiple R-squared: 0.292, Adjusted R-squared: 0.284
## F-statistic: 40.4 on 1 and 98 DF, p-value: 6.65e-09
```

We should see three things in the `lm()`

results:

- The estimate of the Intercept in the model should be very close to the intercept that we specified
- The estimate for the x parameter should be very close to the slope that we specified
- The residual standard error should be roughly similar to the noise standard deviation that we specified