Questions: For the following data set: (a) Compute the least-squares regression line. Round the answers to at least four decimal places. Regression line equation: (b) Which point is an outlier?

Solution Steps

To solve the problem, we need to compute the least-squares regression line for the given data set and identify any outliers. Since the data set is not provided, I'll outline the steps you would take to solve this problem once you have the data.

First, collect the data points that you will use to compute the regression line. The data should be in the form of pairs (x, y).

Calculate the mean of the x-values (\(\bar{x}\)) and the mean of the y-values (\(\bar{y}\)).

Use the formula for the slope of the regression line: \[ b_1 = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}} \]

Calculate the y-intercept of the regression line using the formula: \[ b_0 = \bar{y} - b_1\bar{x} \]

Combine the slope and intercept to form the regression line equation: \[ y = b_0 + b_1x \]

Examine the data points to identify any that do not fit the pattern of the rest of the data. A common method is to look for points that have a large residual (the difference between the observed y-value and the predicted y-value from the regression line).

Final Answer