Deck 15: Questioning the Greatness of Straightness: Nonlinear Relationships

Question 1

Which of the following does not belong in this list?

A) non-linear
B) curvilinear
C) quadratic
D) logistic

Answer 1

D

Question 2

What is the most common format for a simple non-linear regression equation?

A) y = a² + bx
B) y = a + b²x
C) y = a + bx²
D) y = a + bx +cx²

Answer 2

D

Question 3

A researcher hypothesizes that there is a non-linear relationship between hours of internet use per week and happiness. He gets the following equation:
HAPPINESS = 2.37 + .03 (INTERNETHOURS)²
The slope is statistically significant.
What is the best conclusion to make based on this equation?

A) Internet use has a linear relationship with happiness.
B) Internet use has a nonlinear relationship with happiness.
C) Internet use has no relationship with happiness.
D) Cannot determine, since non-squared variable is not present.

Answer 3

D

Question 4

We suspect that the amount you eat (as measured by number of calories) affects happiness in a nonlinear way: those who eat very little will not be happy, those who eat a good amount will be happy, and those who eat a whole lot will not be happy. If we are correct, what form will the model take?

A) HAPPINESS = constant + # (CALORIES) - # (CALORIES)²
B) HAPPINESS = constant - # (CALORIES) + # (CALORIES)²
C) HAPPINESS = constant + # (CALORIES) + # (CALORIES)²
D) HAPPINESS = constant - # (CALORIES) - # (CALORIES)²

Question 5

We suspect that the average monthly outside temperature affects electricity costs in a nonlinear way: during a very cold month electricity costs will be high, during a moderate month electricity costs will be low, and during a very hot month electricity costs will be high. If we are correct, what form will the model take?

A) COST = constant + # (TEMPERATURE) - # (TEMPERATURE)²
B) COST = constant - # (TEMPERATURE) + # (TEMPERATURE)²
C) COST = constant + # (TEMPERATURE) + # (TEMPERATURE)²
D) COST = constant - # (TEMPERATURE) - # (TEMPERATURE)²

Question 6

Here is a set of nested models:
$\text { Dependent Variable: Respondent's Income in 1000's }$

$\begin{array}{lcc}\text { Independent Variable } & \text { Model } 1 & \text { Model } 2 \\\text { Education in years } & 3.57^{* * *} & -3.57^{* * *} \\\text { Education Squared } & --- & .28 * * * \\\text { Hours Worked } & .71^{* * *} & .71^{* * *} \\\text { Constant } & -38.60 & 2.55 \\\text { R-Squared } & .20 & .30\end{array}$

A) Because the linear effect does not lose its statistical significance in Model 2, the linear model is the better model.
B) Neither the linear model nor the non-linear model is better.
C) Because the squared slope is statistically significant, the non-linear model is the better model.
D) Because the R-squared for the non-linear model is much higher than the R-squared for the linear model, the non-linear model is the better model.

Question 7

Using GSS2008 data (respondents aged 18 to 49), here is a non-linear regression equation, using "number of times respondent goes to the zoo" as the dependent variable:
ZOOVISIT = -2.65 + .25 (AGE) - .0038 (AGE)²
According to this equation, who goes to the zoo the most often?

A) an 18-year-old
B) a 25-year-old
C) a 33-year-old
D) a 49-year-old

Question 8

Using GSS2006 data, here is a non-linear regression equation, using "hours per day respondent has to relax" as the dependent variable:
HRSRELAX = 5.83 - .11 (AGE) + .00135 (AGE)²
According to this equation, who has the least amount of time to relax?

A) an 18-year-old
B) a 33-year-old
C) a 41-year-old
D) a 53-year-old

Question 9

What shape does this nonlinear equation take:
Y = -136.82 +10.24(x) - .10(x²)

A) a u-shape
B) an n-shape
C) a w-shape
D) a v-shape

Question 10

What shape does this nonlinear equation take:
Y = 13.62 -.49(x) + .005(x²)

A) a u-shape
B) an n-shape
C) a w-shape
D) a v-shape

Question 11

Using GSS2006 data, here is a non-linear regression equation, using hours of television watched as the dependent variable (EDUC stands for years of education, all slopes are statistically significant):
TVHOURS = 3.36 + .12 (EDUC) -.011 (EDUC)²
Which of the following is the most accurate description of what is going on?

A) People with low levels of education watch a lot of television, then people with moderate levels of education watch less television, and then people with high levels of education watch a lot of television.
B) People with low levels of education watch a little of television, then people with moderate levels of education watch more television, and then people with high levels of education watch a little of television.
C) People with low levels of education watch the most television, and for each additional year of education, hours of television watched goes down by the same amount.
D) People with low levels of education watch the most television, and as education increases, hours of television watched starts going down, slowly at first, and then more and more rapidly.

Question 12

At early levels of income, each additional rise in income produces a sharp rise in financial satisfaction, but at high levels of income, each additional rise in income produces a very small rise in financial satisfaction. This is known as:

A) a quadratic equation
B) diminishing returns
C) a squared term
D) rich people's malaise

Question 13

Here is a set of nested models:
$\text { Dependent Variable: Respondent's Income in 1000's }$
$\begin{array}{lcc}\text { Independent Variable } & \text { Model } 1 & \text { Model } 2 \\\text { Education in years } & 3.57 * * * & 3.37 * * * \\\text { Education Squared } & --- & .02 \\\text { Hours Worked } & .71^{* * *} & .70^{* * *} \\\text { Constant } & -38.60 & -35.60 \\\text { R-Squared } & .20 & .20\end{array}$ What is the most appropriate conclusion to make based on these models?

A) The relationship between education and income is linear.
B) The relationship between education and income is non-linear.
C) There is no relationship between education and income.
D) Education has a larger effect on income than hours worked.

Question 14

To investigate a possible nonlinear relationship, you use an income variable, which is income in dollars, as well as its square. In your SPSS results, the slope for the squared variable is a statistically significant +0.00054. When you write up your results, and calculate examples using your results, which would be the best version of this result to use?

A) +0.0
B) +0.001
C) +0.0005
D) +0.00054

Question 15

Using base 10, what is the log of 1000?

A) 0
B) 1
C) 2
D) 3

Question 16

If we're using income as an independent variable, but our dataset for some reason has people with incomes ranging from $3,000 to $30,000,000. What might we want to do?

A) use a squared version of the income variable in addition to the regular version
B) divide each person's income by 1000
C) use the log of the income variable
D) find another dataset

Question 17

Which of the following variables would you most likely want to log for use in regression?

A) income of respondent
B) number of children a respondent has had
C) age of respondent
D) sex of respondent

Question 18

Volden, Wiseman, and Wittmer's measure of effectiveness concerns:

A) the number of committees on which she serves
B) the number of bills she helps become law
C) the percentage of the vote she gets during re-election
D) her favorability rating among her constituents

Question 19

According to Volden, Wiseman, and Wittmer, who would be the most effective congressperson?

A) a congressman from the majority party
B) a congressman from the minority party
C) a congresswoman from the majority party
D) a congresswoman from the minority party

Question 20

Volden, Wiseman, and Wittmer's research on congresspeople identifies a non-linear relationship between seniority and effectiveness. Which of the following best characterizes what they found?

A) a u-shaped curve: those with low seniority have low effectiveness, those with medium seniority have high effectiveness, and those with high seniority have low effectiveness
B) a ∩-shaped curve: those with low seniority have high effectiveness, those with medium seniority have low effectiveness, and those with high seniority have high effectiveness
C) seniority has a big effect at first, but then this effect tapers off as seniority gets very high
D) seniority has a small effect at first, but then starts to have larger effects as seniority gets very high

Question 21

If you want effective government, according to Volden, Wiseman, and Wittmer, make sure that your congressperson:

A) wins by a small margin
B) wins by a fair amount but not too much
C) wins by a very wide margin
D) wins by running unopposed

Question 22

Eagle's research on congregation size concentrates on:

A) churches
B) temples
C) mosques
D) all of the above

Question 23

Which of the following does Eagle use in his models examining the relationship between congregation size and religious attendance?

A) logistic regression
B) logged variables
C) nonlinear regression
D) all of the above

Question 24

In his research on congregation size, Eagle finds that with regard to the number of regular attenders per congregation, which statistic has grown larger over time:

A) the median
B) the mean
C) the standard deviation
D) all of the above

Question 25

You are a Catholic priest who wants to ensure that your congregants are very likely to attend religious services. According to Eagle's findings, what ideal size church should you aim for?

A) one with 100 members
B) one with 400 members
C) one with 1000 members
D) one with 3000 members

Question 26

We hypothesize that there is a non-linear relationship between internet usage and television usage. Here are two regression models. Interpret them, addressing the hypothesis.
Dependent Variable: Hours Spent Per Week Watching TV

Question 27

Below are two sets of nested models using GSS2006 data. The first set includes only white women, the second set includes only black women.
Dependent Variable: Respondent's Income in Thousands of Dollars
By describing key differences between the effects for white and black women, address this question: for which group is there a more pronounced non-linear relationship?

Question 28

What if you hypothesized that there is a nonlinear relationship between number of dogs you have and your stress level: having a dog or two, or even three lowers your stress level, but then if you have lots and lots of dogs, that ends up causing more stress. Describe the equations you would create to see if this hypothesis is supported, and then describe what the equations would likely look like if the hypothesis was indeed supported.

Question 29

What if you hypothesized that there is a nonlinear relationship between amount of responsibility at work and job satisfaction: having some responsibility at work raises job satisfaction to a level higher than if someone had no responsibility at work; but having too much responsibility at work once again lowers job satisfaction. Describe the equations you would create to see if this hypothesis is supported, and then describe what the equations would likely look like if the hypothesis was indeed supported.

Question 30

You want to use a GSS variable regarding whether or not the respondent favors the legalization of marijuana. You hypothesize that age plays a role with younger people supporting legalization, middle-aged people opposing legalization, and elderly people supporting legalization, but you also hypothesize that this relationship might look different for men and women. Based on all this, describe what regression techniques you would use. Just name them and explain why.

Question 31

Here are two equations using GSS2008 data. The first equation involves only white respondents, and describes a linear relationship (since there was not a non-linear relationship between these variables):
HOURS WORKED PER WEEK = 13.71 + 1.36 (EDUC)
The second equation involves only black respondents, and describes a non-linear relationship (since it performed better than the linear equation for blacks):
HOURS WORKED PER WEEK = -19.93 + 6.85 (EDUC) -.19 (EDUC)²
First, calculate predicted hours worked for each race, for someone with nine years of education, someone with sixteen years of education, and someone with twenty-two years of education. Then, interpret your results.

Question 32

Why does the textbook suggest, if you are using a squared variable for such aspects as income or age, it is important to keep several more decimal places than usual when you are using your slopes to calculate predictions?

Question 33

Describe a situation where you might want to use the log of a variable rather than the original variable.

Question 34

Explain why, using base 10, the log of 10000 is 4.

Question 35

Explain why, in his research on the effects of congregation size, Eagle used the log of congregation size rather than simply the congregation size.