Question

In: Statistics and Probability

A researcher is interested in how income of a parent effects the income of their children....

A researcher is interested in how income of a parent effects the income of their children. They gather data from surveys about household income and they find that from a small sample the following data is true. The left column is the monthly income of person in the thousands and the right is their parent’s average monthly income between the two parents.

Children’s income	Parent’s income average
7	4
7	4
10	3
12	2
6	3
9	1
11	3

What is the independent variable and what it the explanatory variable in this study? (2)

What is the regression line for this data? Please calculate the regression line for this data and interpret the M and B estimates. (5)

Will the regression line perfectly predict the data? Why or Why not? (1)

What does the regression line predict a child’s income will be if their parent’s average income is 10 thousand? (2)

Expert Solution

Answer:-

Given That:-

A researcher is interested in how income of a parent effects the income of their children. They gather data from surveys about household income and they find that from a small sample the following data is true. The left column is the monthly income of person in the thousands and the right is their parent’s average monthly income between the two parents.

What is the independent variable and what it the explanatory variable in this study? (2)

Given,

independnet variable = parents income average

dependnet variable = children 's income

What is the regression line for this data? Please calculate the regression line for this data and interpret the M and B estimates. (5)

x	y
4	7	1.3061	3.4490	-2.122
4	7	1.3061	3.4490	-2.122
3	10	0.0204	1.3061	0.163
2	12	0.7347	9.8776	-2.694
3	6	0.0204	8.1633	-0.408
1	9	3.4490	0.0204	-0.265
3	11	0.0204	4.5918	0.306


Total Sum	20.00	62.00	6.86	30.86	-7.14
Mean	2.86	8.86

sample size n = 7

here,

estimated slope

= -7.1/6.857

= -1.0417

Intercept

so regression line is

Will the regression line perfectly predict the data? Why or Why not? (1)

Correlation coefficient

No, it does nor predict the data perfectly

What does the regression line predict a child’s income will be if their parent’s average income is 10 thousand? (2)

Predicted Y at X = 10 is

= 1.417

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orchestra answered 1 year ago

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