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)

Solutions

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

Thank you for your supporting. Please upvote my answer...


Related Solutions

A researcher is interested in the effects of costume type on the mean amount of Halloween candy that children receive while trick-or-treating.
  A researcher is interested in the effects of costume type on the mean amount of Halloween candy that children receive while trick-or-treating. The researcher randomly selects 20 different children. Half wear cute Halloween costumes, and half wear scary Halloween costumes. The researcher sends the children out to trick-or-treat at 4 houses, then records the number of pieces of candy each child receives. Does costume type affect amount of trick-or-treating candy a child receives? 
A researcher was interested in the effects of caffeine on sleep. She measured how many minutes...
A researcher was interested in the effects of caffeine on sleep. She measured how many minutes it took for ten participants to fall asleep. Half of the participants drank a liter of caffeinated soda before going to sleep while the other half were only allowed to drink water. Summary data of minutes are presented below. Did the caffeine increase the length of time it took to fall asleep (a =.05)?          Water Group Caffeine Group                      18 22                      15...
A researcher is interested in the effects of a new weight loss supplement. Participants in this...
A researcher is interested in the effects of a new weight loss supplement. Participants in this double-blind study are randomly assigned to either a group that receives the new supplement or a group that receives a placebo. Participants are weighed before starting the program. After 6 weeks of taking either the new supplement or the placebo, participants return to the lab to be weighed. Provide the appropriate null and alternative hypotheses. Determine which type of analysis would be appropriate to...
A researcher is interested in the effects of practice on accuracy in a signal detection task....
A researcher is interested in the effects of practice on accuracy in a signal detection task. Participants are tested with no practice, after 1 hour of practice, and after 2 hours of practice. Each person participates in all three conditions. The following data indicate how many signals were accurately detected by each participant at each level of practice.    Amount of practice Participant No Practice 1 Hour 2 Hours 1 3 4 6 2 4 5 5 3 2 3...
A researcher was interested in the effects of alcohol on attractiveness of mate selected (referred to...
A researcher was interested in the effects of alcohol on attractiveness of mate selected (referred to as the beer goggle effect). She compared the rating (by independent raters) on level of attractiveness of the partners that young people chose at a party. She compared a group before using alcohol then after using alcohol. Assessment was whether their chosen partners differed in levels of attractiveness. Higher scores indicated more attractive partners. The attractiveness of partner for each participant (measured by independent...
A researcher is interested in studying the effects of out-of-wedlock childbearing on the subsequent earnings of...
A researcher is interested in studying the effects of out-of-wedlock childbearing on the subsequent earnings of young women. Her sample consists of unmarried women who have had no more than one successful pregnancy (i.e. one kid or one batch of twins). Her dependent variable is annual earnings while her independent variable of interest is each woman’s number of children. She plans to include measures of ethnicity, educational attainment, and local economic factors in her regression equation. There are likely to...
A researcher was interested in the effects of anomie-normlessness or breakdown of rules in a social setting
Research Situation A A researcher was interested in the effects of anomie-normlessness or breakdown of rules in a social setting. She obtained the following suicide rates (the number of suicides per 100,000 population) for five high-anomie, five moderate-anomie, and five low-anomie cities: what is the researchquestion?what is the hypothesis (Null and research statements)what are the two variables and there level of measurments?
Imagine you are a researcher for the Turonis Pizza Company interested in learning the effects of...
Imagine you are a researcher for the Turonis Pizza Company interested in learning the effects of student population on quarterly sales. You collect sales data from a sample of 10 Turonis Pizza Parlor restaurants located near college campuses with known student populations. For the ith observation or restaurant in the sample, x is the size of the student population (in thousands) and y is the quarterly sales (in thousands of dollars). The values for x and y for the ten...
A researcher is interested in the effects of sleep deprivation and caffeine intake on mood. Participants...
A researcher is interested in the effects of sleep deprivation and caffeine intake on mood. Participants were randomly assigned to a sleep condition (normal or deprived) and a caffeine condition (0 cups, 2 cups, or 4 cups). After the manipulations, mood was measured (such that higher numbers indicated better mood). The results were as follows:                    Normal Condition                                      Deprived Condition          0 cups        2 cups        4 cups                    0 cups        2 cups        4 cups             16              18              18                          0               ...
A researcher is interested in looking at the effects of Gatorade consumption on energy use during...
A researcher is interested in looking at the effects of Gatorade consumption on energy use during exercise. To look at this, the researcher split subjects into three groups: No Gatorade, 2 pints of Gatorade, and 4 pints of Gatorade. Subjects were asked to exercise and VO2 max values were recorded. The researcher also was interested in looking at the differential effects of gender. The following data for 48 subjects was collected: Can someone do this in SPSS? No Gatorade 2...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT