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   y
9   7.38
9   6.75
12   13.08
9   7.42
11   7.56
13   8.53
7   5.93
4   5.33
12   8.1
6   6.46
5   5.44

Create a scatterplot of the data. Choose the correct graph below.

A.

05101520250510152025xy

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, 8.5); (5, 5.5); (6, 7); (7, 8); (9, 6); (9, 7.5); (9, 13); (11, 6.5); (12, 7.5); (12, 7.5); (13, 5.5).

B.

05101520250510152025xy

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, 7.5); (9, 7); (12, 13); (9, 7.5); (11, 7.5); (13, 8.5); (7, 6); (4, 5.5); (12, 8); (6, 6.5); (5, 5.5).

C.

05101520250510152025xy

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, 8); (9, 7); (12, 7); (9, 13); (11, 8); (13, 6); (7, 8); (4, 9); (12, 6); (6, 8); (5, 6).

D.

05101520250510152025xy

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: (7.5, 9); (7, 9); (13, 12); (7.5, 9); (7.5, 11); (8.5, 13); (6, 7); (5.5, 4); (8, 12); (6.5, 6); (5.5, 5).

Find the equation of the regression line.

ModifyingAbove y with caretyequals=nothingplus+nothingx

​(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.

The data has a pattern that is not a straight line.

C.

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

D.

There is no characteristic of the data that is ignored by the regression line.

Click to select your answer(s).

Answer 1

a) Scatterplot: Answer B

b)

X	Y	XY	X²	Y²
9	7.38	66.42	81	54.4644
9	6.75	60.75	81	45.5625
12	13.08	156.96	144	171.086
9	7.42	66.78	81	55.0564
11	7.56	83.16	121	57.1536
13	8.53	110.89	169	72.7609
7	5.93	41.51	49	35.1649
4	5.33	21.32	16	28.4089
12	8.1	97.2	144	65.61
6	6.46	38.76	36	41.7316
5	5.44	27.2	25	29.5936
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
97	81.98	770.95	947	656.5932

Sample size, n =	11
x̅ = Ʃx/n =	8.81818
y̅ = Ʃy/n =	7.45273
SSxx = Ʃx² - (Ʃx)²/n =	91.6364
SSyy = Ʃy² - (Ʃy)²/n =	45.6186
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	48.0355

Slope, b = SSxy/SSxx = 0.524196429

y-intercept, a = y̅ - b* x̅ = 2.830267857

Regression equation :   

ŷ = 2.83 + 0.524 x  

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