econ 391 exam 2

Given the following regression equation, what is the expected wage for someone with 14 years of education in a non-STEM occupation? Wage=40+1.2 education+35 stem

$56,800

Now we add a dummy for if you have computer programming knowledge or not. Which of the follow do we expect to have the highest wage? Wage=39+0.6education-0.9stem+30 computer

12 years of school and programming

Suppose you take a random sample of 100 individuals, and find that their mean weight is 75kg. Assume also that the population standard deviation is 4kg. What the Confidence interval at 95% ?

(74.216,75.784) =75+-(1.96)*4/sqrt100

Following is a portion of the computer output for a regression analysis relating Y = number of people who use the public pool to X = the outside temperature. Predict approximately how many people will use the public pool in a day when the temperature is 90 degrees.

131 57.912+0.811838X=57.912+0.81138(90 degrees)=131

Which of the following could NOT be a feasible R-squared?

-1

If we are attempting to observe the effect of hours studied on test scores, which of the following is true?

-Exam score is the dependent variable. -Hours studied will likely not explain 100% of the changes in test scores. -The R-squared of this regression equation would likely be between 0 and 1.

What do we call variables coded as "0" or "1" in regression equations?

-dummy variables -categorical variables -qualitative variables

A sample of 100 footballs showed an average air pressure of 13 psi. The standard deviation of the population is known to be 0.25 psi. With a 0.90 probability, the margin of error is approximately equal to:

0.041 1.645*(0.25)/(sqrt100)=0.041125

Suppose you take a random sample of 100 individuals, and find that their mean weight is 75kg. Assume also that the population standard deviation is 4kg. What is the standard error?

0.40 4/sqrt100)=0.40

In a regression model, if SSE= 150 and SSR= 200, what is the coefficient of determination?

0.57 1-(150/350)=0.57

In a regression analysis, if SSE = 200 and SSR = 300, the coefficient of determination is:

0.60 The formula: 1-(SSE/SST) 1-(200/500)=0.60

In a regression model, if SSE= 100 and SSR=160, the coefficient of determination is:

0.615 SSR/SST=160/260=0.615

For a regression, if SSE = 500 and SST = 1,600. What is R2?

0.68 1,100/1,600=0.68

Suppose you take a random sample of 30 individuals, and find that the mean age is 32 years old. Assume also that the population standard deviation is 4 years. Compute the Standard Error (σ/ n)

0.73 4/sqrt30=0.73

Which value of R2 indicates the best fit?

0.87 -R2 values closest to 1 indicate a good fit and values close to 0 indicate bad fit

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is __________.

0.8780

For a regression, if SSE = 500 and SST = 1,600. What is SSR?

1,100 SSE+SSR=SST 500+SSR=1,600

Suppose you take a random sample of 30 individuals, and find that the mean age is 32 years old. Assume also that the population standard deviation is 4 years. Compute the margin of error for a 95% confidence interval.

1.43 1.96*(4)/sqrt30=1.43

If we have a known standard deviation (σ) of 6.4, and we want a 95% confidence interval (Za/𝟐 ) with a margin of error (MOE) of 2.5, how large (n) of a sample do we need?

25

A 95% confidence interval for ACT scores is calculated based on a random sample of economics undergraduates. The confidence interval is (26, 33). What is the point estimate of the sample of ACT scores from economics students?

29.5 (26+33)/2=29.5

A 95% confidence interval for ACT scores is calculated based on a random sample of economics undergraduates. The confidence interval is (26, 33). What is the margin of error?

3.5 (33-26)/2=3.5

What is the intercept coefficient for the regression equation? Yhat=35+15x1-14x2

35

In a regression model, if SSE= 150 and SSR= 200, what is SST?

350 SST=SSE+SSR 150+200=350

If a regression equation includes 3 dummy variables for nationality, how many different nationalities can we make inferences about from this regression equation?

4

Given that the coefficient of determination for the SuperSki slopes model is 0.54, what is the correct interpretation of this value?

54% of the variation in number of skiers is explained by the X's

What would happen to the margin of error and the confidence interval if the sample size was increased by 100?

The margin of error would decrease and the confidence interval would become thinner.

Given the following excel output, which variable is statistically significant at the 1% level.

Age

If we regressed daily temperature on daily ice cream sales, we would expect to find...

B1>0

The following data show the results of an aptitude test and the grade point average of 10 students. If we were to run a regression where Y = GPA and X = Aptitude score, which of the following is most likely true regarding ß1?

B1>0

Which of the follow is used to represent the Y-intercept in a regression model?

Bo

Given the following excel output, which variable is not statistically significant at the 5% level.

City MPG

For a 95% confidence interval, if we increase the sample size, the width of the interval will increase.

False As we increase the denominator, the margin of error will go down, giving us a thinner confidence interval.

If the value of R2 is negative, this means that there is a negative correlation

False R2 can only take on values between 0 and 1

In multivariable regression, only continuous variables can be used as independent variables.

False We can also use dummy variables for multivariate regression

The R2 will fall if you add an additional independent variable (explanatory variable) that is not statistically significant.

False, any additional variable will increase or keep the R squared the same value

One example of a quantitative variable would be a dummy variable that signifies whether an individual is a registered Republican or not.

False, whether someone is Republican or not is categorical, not quantitative

Which of the following variables is most likely a dummy variable?

Gender

Which of the following regarding the adjusted !" is true?

It adjusted for the number of predictors in the model.

How do we interpret the coefficient on Delta Airlines? (note: Southwest is unincluded category)

On average, Delta airline tickets cost 72 dollars more than Southwest.

Given the following regression equation, what is the interpretation on STEM? Wage is measured in $1000s, Education in years, and STEM is a dummy for if you work in a STEM occupation. Wage=40+ 1.2 education+35 Stem

On average, all else constant, STEM occupations make $35,000 more than non- STEM occupations

Y=40350+4.1X1-.55X2 Given the regression equation, what is the interpretation of B2?

On average, an additional unit of X_2 decreases Y by 0.55 (all else constant).

Which of the following P-values will lead to a rejection of the null hypothesis at the 95% confidence level?

P-value=0.04

Which of the following statements regarding R-squared is NOT true?

R-squared is always smaller than or equal to adjusted R-squared.

Which of the following variables is significant at the 10% ?

Temperature

Which of the following statements about the coefficient of determination (R2) is correct?

The coefficient of determination quantifies the fraction of variation in the response variable that is explained by changes in the explanatory variables.

Which of the following best defines "residual"?

The difference between the observed value of the dependent variable and the predicted value

What is Bo?

The intercept of the simple regression equation

Why must an error term be included in regression equations?

There are factors affecting the dependent variable which are not included in the regression equation.

Given a coefficient of determination, R2 = 0.87, we can say that our model is a good fit.

True The coefficient of determination determines the fitness of the model. 0.87 is a high coefficient of determination, so we can say that this model is a good fit.

A regression model estimates the coefficients we are interested in by minimizing the sum of the squared residuals (or the Sum of Squared Errors).

True, the algorithm using in a regression model is minimizing the sum of the squared residuals to calculate the coefficient estimates

If we ran a simple linear regression of X on Y and found a highly statistically significant result, we could conclude which of the following?

changes in X are associated with changes in Y

Which of the following statements is FALSE?

We can always capture 100% of the variation in our dependent variable in a regression equation.

Following is a portion of the computer output for a regression analysis relating Y = number of people who use the public pool to X = the outside temperature. What is the equation for this model?

Y (hat)=57.912+0.81138X

What is the expected change to 𝑌hat if both independent variables increase by 1 unit? yhat=35+15x1-14x2

Y hate will increase by 1 unit

Given that Y is the dependent variable in an equation, what is the difference between Y ̂ and Y?

Y ̂ is a predicted value, while Y is known.

Given the following excel output, how would you write the equation?

Y=-400+25X_1+30X_2 "-2 " X_3

Which equation describes the multiple regression equation?

Y=Bo+B1X1+B2X2+e

What is the expected change to 𝑌hat if 𝑥1 decreases by 2 units? yhat=35+15x1-14x2

Yhat decreases by 30 units -on average holding all else constant, if x1 increases by 1 unit

In the model Y = β0 + β1 X + β2 D + β3 X*D + ε, the interaction variable causes _______ ________________________________.

a change in just the slope

which statement is true of dummy variables?

a dummy variable can only be 0 or 1

which of the following would most likely be considered a dummy variable?

country of origin

You run a regression predicting wage based on a number of individual characteristics including gender and years of education. You suspect that the value of education could be different for men and women. How could you test this claim?

add an interaction variable between education and gender

When the level of confidence decreases, the margin of error:

becomes smaller

Which of the following variables is most likely not be a dummy variable?

distance from home to work

Which of the following is the reason a reference or base group must be selected and excluded from the model when using dummy variables?

if one is not chosen, then the coefficients would not be interpretable

A multiple regression model has the form: Yhat = 5 + 6x + 7w As x increases by 1 unit (holding w constant), y is expected to _________.

increase by 6 units

Which of the following would cause a confidence level to narrow?

increase the sample size

Which of the following will increase the width of a confidence interval?

increasing the level of confidence

Whether a dummy variable takes the value "0" or "1" affects which of the following in a regression equation?

intercept

Larger values of R2 imply that observations are more closely grouped about the:

least squares errors line

The least squares criterion is _________.

min E(Yi-Yhati)^2

The mathematical equation that explains how the dependent variable Y is related to several independent variables X1, X2 ,...,Xp and the error term ε is a(n) _____.

multiple regression equation

A variable that cannot be measured in numerical terms is called a _____.

qualitative variable

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is called a(n):

residual The residual is the difference between the predicted and true value at a given data point. The other choices are irrelevant to residual.

A decrease in which of the following increases the margin of error?

sample size

Which of the following variables would most likely NOT be considered a Dummy Variable?

speed in miles per hour

Consider a simple regression equation Yhat=Bhat0+bhat1X What is YHat?

the predicted value of Y, given a specific value of X

Which factor does not affect the size of the margin of error?

the same mean

In multiple regression analysis, __________________.

there can be several independent variables, but only one dependent variable

In a simple linear regression model, we find that β1 is not significantly different from zero. Which of the following can we conclude?

there is no linear relationship between X and Y

Suppose you have two variables in a model, INCOME, the dependent variable which measures income and COLLEGE (independent variable), which takes a value of 1 if the person has completed college and 0 if they have not completed college. What is the comparison/benchmark group in this case?

those who have not completed college -We leave out a dummy variable for whether a person has not completed college, so they are our comparison/benchmark group.

Which of the following is our goal when performing regression analysis?

to minimize the sum of squared residuals (SSE)

In a simple regression model, the phrase, "holding all else constant" should not be used in the interpretation of the slope coefficient (𝛽ଵ).

true Since we are not including any other variables in the model, we are not holding them constant when we estimate 𝜷𝟏.

Suppose that you ran a regression with only 𝑥1 and found R2 = 0.67. When you ran the model with both independent variables, R2 = 0.68. What can we say about the importance of adding x2?

x2 is not an important addition to the model because it does not increase the fitness of the model significantly. -Since the value of the R2 does not increase by much, we know that adding 𝑿𝟐 does not contribute much to explaining the changes in Y