O Type here to search Think about how dose the Ine Y -2x 11 is to the sample poi
ID: 3227515 • Letter: O
Question
O Type here to search Think about how dose the Ine Y -2x 11 is to the sample points. Look at the graph and find each point's vertical distance from the line. the point sts above the line, the distance is positive; ifthe point sits below the line, the distance is negative. The sum of the vertical distances between the sample points and the orange line is and the sum of the squared vertical distances between the sample points and the orange line is On the graph, place the black point (x symbol) on the graph to plot the point (M where M, is the mean year for the four students (1, 2, 3, and 4) in the sample and Mr is the mean hours of course work per dass for the four students (8, 8, 7, and 5) in the sample. Then use the green line (triangle symbols toplot the line that has the same shre as (is parallel to) the line Y x +11, but with the additional property that the vertical distances between the points and the line sum to o. To plot the line, drag the green line onto the graph. Move the green triangles to adjust the slope through the point (Mix MY) The line you just plotted The suma the squared vertical distances between the sample p and the wine that you ust potted is which of the following describes the plotted line wth the smaaesttotal squared error? Q Neither-the two lines fit the data equally wel The 2x 11 dstancesequal to o line you plotted that has a sum of the suppose you fit the regression ine to the four sample points on the graph on the basis of your work so far, being as speork as you can be, you know that the total squared emor isExplanation / Answer
Sum of vertical distances between the sample points and the orange line is = (-1) + (+1) + (2) + (2) = 4
Sum of the squared vertical distances between the sample points and the orange line is = 12 + 12 + 22 +22 = 10
Mx = 2.5 and My = 7
so slope is same so line equation must be Y = -2X + C
by putting value X = 2.5 and Y = 7
line equation is 7 = - 2* 2.5 + C => C = 12
line equation y = -2x + 12
Sum of vertical distances between the sample points and the new line is = (2) + (0) + (-1) + (-1) =0
Sum of the squared vertical distances between the sample points and the new line is = 22 + 02 + 12 +12 = 6
So the smallest total squared error is the line you plotted that has a sum of the distances equal to 0. Option C is correct.
Here I fit the regression line to the four sample points on the graph.
Regression line is y = -x + 9.5
where total squared error = 4 * (0.5)2= 1
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