Question

Complete parts (a) through (c) using the following data.

Row 1: 1 3 3 4 4 4 5 6 6 7

Row 2: 90 82 76 76 90 72 80 90 55 70

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.

^

Y = ___x +(___)

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.

B.) Find the equation of the regression live 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.

^

Y = ____x + (___)

Construct a scatter plot of the data and draw the regression line. Plot row 2 on the horizontal axi and Row 1 on the vertical axis.

C.) What effect does switching the explanatory and response variables have on the regression line?

1.) The sign and value of m is unchanged, but the value of b changes.

2.) The value of m is unchanged, but the sign of m and value of b change.

3.) the sign of m is unchanged, but the values of m and b change.

4.) The value of b is unchanged, but the sign and value of m change.

5.) The sign and value of m and the value of b all change.

6.) Nothing changes.

Answer 1

A)

The following data are passed:

X	Y
1	90
3	82
3	76
4	76
4	90
4	72
5	80
6	90
6	55
7	70

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	1	90	90	1	8100
	3	82	246	9	6724
	3	76	228	9	5776
	4	76	304	16	5776
	4	90	360	16	8100
	4	72	288	16	5184
	5	80	400	25	6400
	6	90	540	36	8100
	6	55	330	36	3025
	7	70	490	49	4900
Sum =	43	781	3276	213	62085

Based on the above table, the following is calculated:

Therefore, we find that the regression equation is:

Graphically:

B)

The following data are passed:

X	Y
90	1
82	3
76	3
76	4
90	4
72	4
80	5
90	6
55	6
70	7

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	90	1	90	8100	1
	82	3	246	6724	9
	76	3	228	5776	9
	76	4	304	5776	16
	90	4	360	8100	16
	72	4	288	5184	16
	80	5	400	6400	25
	90	6	540	8100	36
	55	6	330	3025	36
	70	7	490	4900	49
Sum =	781	43	3276	62085	213

Based on the above table, the following is calculated:

Therefore, we find that the regression equation is:

Graphically:

C)

3.) the sign of m is unchanged, but the values of m and b change.

Please let me know in comments in case anything is unclear. Will reply ASAP. Do upvote if satisfied!