Applied Statistical Methods - Solution 3

Problem 1: Simple Linear Regression

Use the data on Width and Height that we collected during the class to fit a linear regression model to the data. Use the formula derived in class to compute estimates \(\widehat{b}_0\) and \(\widehat{b}_1\) for the intercept (\(b_0\)) and the slope (\(b_1\)) that define the linear regression line. Verify the obtained results using the function lm() in R.

Tasks

• Read data from https://charlotte-ngs.github.io/asmasss2024/data/asm_width_height.csv using the function read.table()

• Compute estimate \(\widehat{b}_1\) for the slope \(b_1\) using the formula from class given as

\[\widehat{b}_1 = \frac{(xy). - N\bar{x}.\bar{y}.}{(x^2). - N\bar{x}.^2}\]

• Compute estimate \(\widehat{b}_0\) for the slope \(b_0\) using the formula from class given as

\[\hat{b}_0 = \bar{y}. - \hat{b}_1\bar{x}. \]

• Validation with R