Question

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

Row 1 Row 2

2 93

2 87

2 79

5 78

5 95

5 66

6 74

6 84

7 56

8 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.

y =_____x+ ( _____ )

​(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.

​(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.

y = ______ x+ ( _____ )

​(Round to three decimal places as​ needed.)

Construct a scatter plot of the data and draw the regression line. Plot Row 2 on the horizontal axis and Row 1 on the vertical axis. Choose the correct graph below.

​(c) What effect does switching the explanatory and response variables have on the regression​ line? Choose the right answer below

A.The sign of m is​ unchanged, but the values of m and b change.

B.The sign and value of m is​ unchanged, but the value of b changes.

C.The value of b is​ unchanged, but the sign and value of m change.

D.The value of m is​ unchanged, but the sign of m and value of b change.

E.The sign and value of m and the value of b all change.

F.Nothing changes.

Answer 1

		X	Y		Yr=-3.995X+96.577
		Row1	Row2(Y axis)	ROW 1	Regression Line
		2	93	2	88.587
		2	87	2	88.587
		2	79	2	88.587
		5	78	5	76.602
		5	95	5	76.602
		5	66	5	76.602
		6	74	6	72.607
		6	84	6	72.607
		7	56	7	68.612
		8	62	8	64.617
	(a)
		Row1 Xaxis
		Row2-Y axis
		EQUATION:
		Y=mX+b
		m=Slope
		b=intercept
		Using "Regression "tool of Data analyis:
		(Click "Data" , then click "Data Analysis".Select "Regression")
		Input Y range Row2,Input X range Row 1, then click "OK"
		We get the following output
					SUMMARY OUTPUT
					Regression Statistics
					Multiple R	0.65912205
					R Square	0.43444187
					Adjusted R Square	0.36374711
					Standard Error	10.3947044
					Observations	10
					ANOVA
						df	SS	MS	F	Significance F
					Regression	1	664.001	664.001	6.145319	0.038173
					Residual	8	864.399	108.0499
					Total	9	1528.4
						Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
					Intercept	96.5769231	8.405236	11.49009	2.98E-06	77.19441	115.9594	77.19441	115.9594
					X Variable 1	-3.9951923	1.611631	-2.47898	0.038173	-7.71162	-0.27877	-7.71162	-0.27877
		X variable 1=	Slope=m		-3.995192308
		Intercept=b=			96.57692308
		EQUATION:
		Y=-3.995X+96.577
	(b)	Row2 Xaxis
		Row1-Y axis
		EQUATION:
		Y=mX+b
		m=Slope
		b=intercept
		X	Y	Xr	Yr=-0.109Xr+13.217
		Row2	Row1(Y Axis)	Row2	Regression Line
		93	2	56	7.113
		87	2	62	6.459
		79	2	66	6.023
		78	5	74	5.151
		95	5	78	4.715					`
		66	5	79	4.606
		74	6	84	4.061
		84	6	87	3.734
		56	7	93	3.080
		62	8	95	2.862
		Using Regression toolof Data Analysis
		Input Y range Row1,Input X range Row 2, then click "OK"
					SUMMARY OUTPUT
					Regression Statistics
					Multiple R	0.65912205
					R Square	0.43444187
					Adjusted R Square	0.36374711
					Standard Error	1.7149059
					Observations	10
					ANOVA
						df	SS	MS	F	Significance F
					Regression	1	18.07278	18.07278	6.145319	0.038173
					Residual	8	23.52722	2.940902
					Total	9	41.6
						Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
					Intercept	13.2165663	3.438217	3.844018	0.004919	5.288024	21.14511	5.288024	21.14511
					X Variable 1	-0.1087412	0.043865	-2.47898	0.038173	-0.20989	-0.00759	-0.20989	-0.00759
		X variable 1=	Slope=m		-0.108741167
		Intercept=b=			13.21656634
		EQUATION:
		Y=-0.109X+13.217
	.(c)	A.The sign of m is​ unchanged, but the values of m and b change.
		X	Y		Sign of m	Value of m	Value of b
		Row 1	Row 2		Negative	3.99519231	96.57692
		Row 2	Row 1		Negative	0.10874117	13.21657