This Question: 5 pts 4 of 15 (1 complete) This Test: 48 pts possi Question Help

Question

This Question: 5 pts 4 of 15 (1 complete) This Test: 48 pts possi Question Help Complete parts (a) through (c) using the following data Row 1 Row 2 6 6 95 83 82 76 98 75 72 90 62 (a) Find the equation of the regression line for the given data, letting Row 1 represent the x-values and Row 2 the y-values. Sketch a scatter plot of the data and draw the regression line Input the values of the slope and intercept for the regression line when Row 1 represents the x-values (Round to three decimal places as needed.) Construct a scatter plot of the data and draw the regression line. Plot Row 1 on the horizontal axis and Row 2 on the vertical axis. Choose the correct graph below OA, 50 100 100 (b) Find the equation of the regression line for the given data, letting Row 2 represent the x-values and Row 1 the y-values. Sketch a scatter plot of the data and draw the regression line Input the values of the slope and intercept for the regression line when Row 2 represents the x-values (Round to three decimal places as needed.)

Explanation / Answer

Here to get linear regression line equation we need x, y, xy, x2

Here the table for these values are

Here let say the line equation is

y^ = a + bx

so here,

a =  [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = [794 * 209 - 43 * 3299] / [ 10 * 209 - 432]  

a = 24089/ 241 = 99.954

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [10 * 3299 - 43 * 794] / [ 10 * 209 - 432]  

b = -1152/ 241 = -4.780

so line equation is

y^ = -4.780 + 99.954

Option C is the correct scatter plot here

(b) Now we will gain calculate the new regression line with the help of new x, y, xy, x2

Here,

Here let say the line equation is

y^ = a + bx

so here,

a =  [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = [43 * 64492 - 794* 3299] / [ 10 * 64492 - 7942]  

a = 153750/14484 = 10.615

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [10 * 3299 - 43 * 794] / [ 10 * 64492 - 7942]  

b = -1152/ 14484 = -0.079

so new line equation is

y^ = 10.615 - 0.079x

Hee the correct scatter plot is A.

(c) Here everything changes. Sign and value of m change and b also chnge.

Row 1 (x) Row 2 (y) x^2 xy 1 95 1 95 3 83 9 249 3 82 9 246 4 76 16 304 4 98 16 392 5 75 25 375 5 72 25 360 6 90 36 540 6 61 36 366 6 62 36 372 Sum 43 794 209 3299

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