Linear equations and the regression line **Please answer all the questions and g

Question

Linear equations and the regression line

**Please answer all the questions and graph the sum of distances and (Mx,My), thank you!

Aa Aa E. 4. Linear equations and the regression line Suppose a graduate student does a survey of undergraduate study habits on her university campus. She collects data on students who are in different years in college by asking them how many hours of course work they do for each class in a typical week. A sample of four students provides the following data on year in college and hours of course work per class: Student Year in College Course Work Hours per Class Freshman (1) Sophomore (2) Junior (3) Senior (4) A scatter plot of the sample data is shown here (blue circle symbols). The line Y 2X 11 is shown in orange. HOURS 10 0 Sum of Distances Mx, My) YEAR Clear All

Explanation / Answer

The sum of the vertical distances between the sample points and orange line is (-1) +(+1) + ( +2) +(+2) = 4 , and the sum of the squared vertical distances between the sample points and the orange line is

(-1)2 + (+1)2 + (+2)2+ (+2)2 = 10

Mx = (1+ 2 + 3 + 4)/ 4 = 2.5

My = (8+8+7+5)/4 = 7

Vertical distances between the points and the line sum to 0.

So the line is Y = -2X + 12 through the point ( 2.5, 7)

The sum of the squared vertical distances between the sample points and the line just plotted is = (-2)2 + ( 0)2 + (1)2 + (1)2 = 6

Option (a) is correct that the line you plotted has a sum distances equal to 0 has the smallest total squared error.

SUppose you fit the regression line to the four sample points on the graph. On the basis of your work so far, being as specific as you can be, you know that the totla squared error is less than or equal to 6. (option B)

It is because for any regression line, mean error is always 0 but the target is to minimize the mean squared error. So any regression line which is a perfect fit will have mean square error less than 6.

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