Question

data on y = time to complete a task (in minutes) and x = number of hours of sleep on the previous night were used to find the least - squares regression line. the equation of the line was $hat{y}=12 - 0.36x$. for this data set, would the sum of squared deviations from the line $y = 12.5-0.5x$ be greater or less than the sum of squared deviations from the least - squares regression line? explain your choice. (hint: think about the definition of the least - squares regression line.) the sum of the squared vertical deviations from the line $y = 12.5 - 0.5x$ would be larger than the sum of the squared vertical deviations from the least - squares regression line $hat{y}=12 - 0.36x$ because, by definition, the least - squares regression line is the line with the maximum value for the sum of the squared vertical deviations from the line. the sum of the squared vertical deviations from the line $y = 12.5 - 0.5x$ would be smaller than the sum of the squared vertical deviations from the least - squares regression line $hat{y}=12 - 0.36x$ because, by definition, the least - squares regression line is the line with the maximum value for the sum of the squared vertical deviations from the line. the sum of the squared vertical deviations from the line $y = 12.5 - 0.5x$ would be smaller than the sum of the squared vertical deviations from the least - squares regression line $hat{y}=12 - 0.36x$ because, by definition, the least - squares regression line is the line with the minimum value for the sum of the squared vertical deviations from the line. the sum of the squared vertical deviations from the line $y = 12.5 - 0.5x$ would be larger than the sum of the squared vertical deviations from the least - squares regression line $hat{y}=12 - 0.36x$ because, by definition, the least - squares regression line is the line with the minimum value for the sum of the squared vertical deviations from the line. resources read it

Explanation:

The least - squares regression line is defined as the line that minimizes the sum of the squared vertical deviations from the line. So, any other line will have a larger sum of squared vertical deviations.

Answer:

The sum of the squared vertical deviations from the line $y = 12.5-0.5x$ would be larger than the sum of the squared vertical deviations from the least squares regression line $\hat{y}=12 - 0.36x$ because, by definition, the least squares regression line is the line with the minimum value for the sum of the squared vertical deviations from the line.