Question

Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x 9 8 11 9 10 13 6 4 12 7 5 y 7.24 7.08 13.32 7.2 7.47 8.99 5.84 5.23 8.55 6.61 5.62 Create a scatterplot of the data. Choose the correct graph below. A. 0510152025 0510152025xy A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (9, 7); (8, 7); (11, 13.5); (9, 7); (10, 7.5); (13, 9); (6, 6); (4, 5); (12, 8.5); (7, 6.5); (5, 5.5). B. 0510152025 0510152025xy A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (4, 13.5); (5, 7.5); (6, 7); (7, 9); (8, 8.5); (9, 5.5); (9, 7); (10, 5); (11, 6); (12, 6.5); (13, 7). C. 0510152025 0510152025xy A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (7, 9); (7, 8); (13.5, 11); (7, 9); (7.5, 10); (9, 13); (6, 6); (5, 4); (8.5, 12); (6.5, 7); (5.5, 5). D. 0510152025 0510152025xy A scatterplot has a horizontal x-scale from 0 to 25 in intervals of 1 and a vertical y-scale from 0 to 25 in intervals of 1. Eleven points are plotted with approximate coordinates as follows: (9, 6); (8, 7); (11, 5); (9, 9); (10, 6); (13, 7); (6, 14); (4, 8); (12, 7); (7, 9); (5, 7). Find the equation of the regression line. ModifyingAbove y with caret equalsnothingplusnothing x ​(Round the constant two decimal places as needed. Round the coefficient to three decimal places as​ needed.) Identify a characteristic of the data that is ignored by the regression line. A. There is no trend in the data. B. There is no characteristic of the data that is ignored by the regression line. C. The data has a pattern that is not a straight line. D. There is an influential point that strongly affects the graph of the regression line. Click to select your answer(s).

Answer 1

Following is the scatter plot:

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	9	7.24	81	52.4176	65.16
	8	7.08	64	50.1264	56.64
	11	13.32	121	177.4224	146.52
	9	7.2	81	51.84	64.8
	10	7.47	100	55.8009	74.7
	13	8.99	169	80.8201	116.87
	6	5.84	36	34.1056	35.04
	4	5.23	16	27.3529	20.92
	12	8.55	144	73.1025	102.6
	7	6.61	49	43.6921	46.27
	5	5.62	25	31.5844	28.1
Total	94	83.15	886	678.2649	757.62

Sample size: n=11

Now,

Slope of the regression equation is

and intercept of the equation will be

So the regression equation will be

y'=2.70+0.569*x

Correct option:

D. There is an influential point that strongly affects the graph of the regression line.