Question

Use the following data

Row 1- 1, 3, 3, 3, 5, 5, 6, 6, 7, 8

Row 2- 94, 87, 83, 73, 91, 68, 74, 82, 65, 65

A. Find the equation of the regression line for the given data, 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 for the regression line when Row 1 represents the x values

Y= __x + (__)

Construct a scatter plot. Row 1 on the horizontal axis and row 2 on the vertical axis.

B. Find 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 c values

Y= __x + (__)

Construct the scatter plot. Row 2 on the horizontal line and row 1 on the vertical line

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

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

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

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

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

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

f. Nothing changes

Answer 1

Let’s use SPSS to solve this problem

STEPS

1. Enter the given data in to SPSS data view window
2. we created two variables so that we could enter our data X as independent variable, and Y as the dependent variable.
3. Go to Analyze >>>> Regression >>>> Linear Regression >>>> Send Y variable to dependent variable pan and X variable to independent variable pan.
4. Finally Click on OK button the RESULT will be displayed in the output Window and the result shown below

we can observe both the scatter plots are negatively correlated even if the variables x and y switched.

correlation between variables x and y is -0.705.   

Slope and intercept values of the regression model and Scatter plots are shown below.

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	94.544	6.351		14.887	.000
	x	-3.477	1.238	-.705	-2.808	.023
Dependent Variable: y Input the values of the slope for the regression line when Row 1 represents the x values Y= __x + (__) i.e., Y= -3.477 X + 94.544   Scatter plot when Row 1 i.e., (X) on the horizontal axis and Row 2 i.e., (Y) on the vertical axis.
B) Similarly solve the regression equation as above just by changing the variables i.e., Y as independent variable, and X as the dependent variable.

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	15.863	4.008		3.957	.004
	x	-.143	.051	-.705	-2.808	.023
a. Dependent Variable: y

Slope and intercept for the regression line when Row 2 represents the c values

Y= __x + (__)

Y= -0.143 X + 15.863

Scatter plot when Row 2 i.e., (X) on the horizontal line and row 1 (Y) on the vertical line

(c) Option-C

From the two regression equations of question-A and question-B i.e., Y=MX+B we get,

Y= -3.477 X + 94.544  

Y= -0.143 X + 15.863

We can observe The sign of ‘m’is unchanged, but the values of ‘m’ and ‘b’ change

So the answer for 3^rd bit is option – C