Question 1

When using the p-value method for hypothesis testing,if the calculated p-value is smaller than the chosen significance level,then you should

Accepted Answer

A) reject the null hypothesis. 
B) fail to reject the null hypothesis. 
C) choose a smaller significance level that is less than the p-value. 
D) calculate a new p-value that is larger than the chosen significance level. 
A) reject the null hypothesis. 
B) fail to reject the null hypothesis. 
C) choose a smaller significance level that is less than the p-value. 
D) calculate a new p-value that is larger than the chosen significance level. A

Question 2

Why are each of the individual simple linear regression model assumptions important? Explain.

Accepted Answer

Assumption 1:If the model is not correctly specified then the estimates based on it will not be meaningful or true.

Assumption 2:If the data is not collected through random sampling then a model that is specified conditional on the observations not being related to each other then the estimated coefficients will be wrong.

Assumption 3:If the independent variable does not vary then $\hat { \beta } _ { 1 }$ 
is not defined and therefore an estimate cannot be derived.

Assumption 4:If the average value of the error term is not equal to zero then the estimates on average will be wrong on average.

Assumption 5:If the error term is related to the independent variables,then if the independent variable increases by one unit then the error term will increase as well,therefore not allowing for a measurement of how the independent variable affects the dependent variable holding other factors constant (because the error term changed as well).

Assumption 6:If the variance of the error term is not constant then OLS,that treat all observations the same,is not the most preferred method to estimate the regression model.

Question 3

A counselor working with teenagers is interested in the relationship between anxiety and depression.The counselor administers a depression and anxiety test to each teenager.The scores obtained from the administration of the two inventories are given below. $$\begin{array} { | c | c | } 
\hline \text { Anxiety } & \text { Depression } \
\hline 22 & 16 \
\hline 12 & 8 \
\hline 68 & 33 \
\hline 10 & 6 \
\hline 5 & 5 \
\hline 53 & 24 \
\hline 44 & 18 \
\hline 37 & 17 \
\hline 0 & 2 \
\hline 21 & 14 \
\hline 64 & 31 \
\hline 33 & 17 \
\hline 55 & 30 \
\hline 18 & 13 \
\hline 3 & 3 \
\hline 4 & 4 \
\hline 11 & 7 \
\hline 13 & 9 \
\hline 7 & 5 \
\hline
\end{array}$$ 
 $\begin{array}{lrr} 
\text { The summary statistics are }\
& \text { Anxiety } & \text { Depression } \
\text { Sample mean } & 25.2632 & 13.7895 \
\text { Standard deviation } & 21.9895 & 9.8464
\end{array}$

$\sum_{i=1}^{19}\left(x_{1}-\bar{x}\right)\left(y_{i}- \bar{y}\right)=3828.0526$

If an individual had an anxiety score of 40,what is a 95% confidence interval for the mean predicted value?

Accepted Answer

$$ dep\widehat {ress}ion = 2.6782 + 0.4398 \cdot \text { anxiety } = 2.6782 + ( 0.4398 ) \cdot ( 40 ) = 20.27$$ 
This means if a person scores 40 on the anxiety test they are predicted to score 20.27 on the depression test.

critical value = 2.11

standard error = 0.5298

95% confidence interval for the mean value is (19.1531,21.2889).

Question 4

A sampling distribution is

Accepted Answer

A) the distribution of a parameter. 
B) the distribution of a statistic. 
C) the standard deviation of a statistic. 
D) the standard deviation of the estimated slope coefficient. 
A) the distribution of a parameter. 
B) the distribution of a statistic. 
C) the standard deviation of a statistic. 
D) the standard deviation of the estimated slope coefficient.

Question 5

The t-statistic for the individual significance of the estimated slope coefficient$\hat { \beta } _ { 1 }$Is

Accepted Answer

A) the standard error of the estimated slope coefficient. 
B) the estimated slope coefficient. 
C) the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient. 
D) the ratio of the estimated slope coefficient to the variance of the estimated slope coefficient. 
A) the standard error of the estimated slope coefficient. 
B) the estimated slope coefficient. 
C) the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient. 
D) the ratio of the estimated slope coefficient to the variance of the estimated slope coefficient.

Question 6

Figure:
Suppose you regress U.S.annual real GDP ($ billions)on U.S.annual real defense expenditures ($ millions)and that you get the following results. SUMMARY OUTPUT

$\begin{array}{lc}
\hline \text { Regvessiait Statistics } & \
\hline \text { Muatiple R. } & 0.523337059 \
\text { R Sqare } & 0.273881677 \
\text { Adjusted R Square } & 0.263508558 \
\text { Standard Error } & 3201.551247 \
\text { Obsenvations } & 72 \
\hline
\end{array}$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & \text { of } & S S & \text { MS } & F & \text { Siguffecance } F \
\hline \text { Regressice } & 1 & 270629128.2 & 270629128.2 & 26.4030211 & 2.39636 \mathrm{E}-06 \
\text { Residual } & 70 & 717495127 & 10249930.39 & & \
\text { Total } & 71 & 988124255.3 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coeffieients } & \text { Staudard Errar } & t \text { Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper } 95 \% 6 \
\hline \text { linercept } & 1273.293919 & 979.7967762 & 1.299548998 & 0.198019186 & -680.8491085 & 3227.436946 \
\text { Real Defense Expesdtures (milions) } & 0.013659042 & 0.002658235 & 5.138387013 & 2.39636 \mathrm{E}-06 & 0.008357359 & 0.018960725 \
\hline
\end{array}$

$\text { Figure } 5.1$

-Based on the Excel output in Figure 5.1,you should conclude that

Accepted Answer

A) the estimated intercept is statistically significant. 
B) the estimated intercept is not statistically significant. 
C) the estimated slope coefficient is not statistically significant. 
D) the estimated sample regression function is not statistically significant. 
A) the estimated intercept is statistically significant. 
B) the estimated intercept is not statistically significant. 
C) the estimated slope coefficient is not statistically significant. 
D) the estimated sample regression function is not statistically significant.

Question 7

What is the intuition behind the critical-value method of hypothesis testing? Explain.

Accepted Answer

If the null hypothesis is true,then the

Question 8

The logic behind the F-test for the overall significance of the estimated sample regression function is that if the estimated sample regression function explains a significant amount of the variation in the dependent variable,then

Accepted Answer

A) the regression F-statistic should be small. 
B) the MSUnexplained should be large relative to the MSExplained. 
C) the MSExplained should be large relative to the MSUnexplained. 
D) total sum of squares should be large. 
A) the regression F-statistic should be small. 
B) the MSUnexplained should be large relative to the MSExplained. 
C) the MSExplained should be large relative to the MSUnexplained. 
D) total sum of squares should be large.

Question 9

The logic behind the t-test for the individual significance of the estimated slope coefficient $\hat { \beta } _ { 1 }$
Is that if the estimated slope coefficient is likely to be different from 0,then

Accepted Answer

A) the estimated slope coefficient should be large. 
B) the estimated standard error should be large. 
C) the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient should be small. 
D) the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient should be large. 
A) the estimated slope coefficient should be large. 
B) the estimated standard error should be large. 
C) the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient should be small. 
D) the ratio of the estimated slope coefficient to the standard error of the estimated slope coefficient should be large.

Question 10

What is the intuition behind the confidence interval method of hypothesis testing? Explain.

Accepted Answer

The 95% confidence interval means that 9

Question 11

The p-value method for hypothesis testing relies on the fact that

Accepted Answer

A) if the null hypothesis is false,then it is very unlikely to observe a p-value smaller than the chosen significance level. 
B) if the null hypothesis is true,then it is very unlikely to observe a p-value larger than the chosen significance level. 
C) if the null hypothesis is true,then it is very unlikely to observe a p-value smaller than the chosen significance level. 
D) if the alternative hypothesis is true,then it is very unlikely to observe a p-value smaller than the chosen significance level. 
A) if the null hypothesis is false,then it is very unlikely to observe a p-value smaller than the chosen significance level. 
B) if the null hypothesis is true,then it is very unlikely to observe a p-value larger than the chosen significance level. 
C) if the null hypothesis is true,then it is very unlikely to observe a p-value smaller than the chosen significance level. 
D) if the alternative hypothesis is true,then it is very unlikely to observe a p-value smaller than the chosen significance level.

Question 12

Figure
Suppose you regress obesity rates for the 50 states and the District of Columbia on the percentage of adults who have earned a Bachelor's degree and that you get the following results. SUMMARY OUTPUT
$\begin{array}{lr}
\hline \text { Regression Staristies } & \
\hline \text { Multple R. } & 0.755633848 \
\text { R. Square } & 0.570982512 \
\text { Adjasted R. Square } & 0.562227053 \
\text { Standard Erroe } & 2.233627219 \
\text { Observations } & 51 \
\hline
\end{array}$

$\text { ANOVA }$
$\begin{array}{lrrrrrr} 
\hline & \text { df } & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 1 & 325,3608375 & 325.3608375 & 65.21445826 & 1.46476 \mathrm{E}-10 \
\text { Residual } & 49 & 244.465437 & 4.989090551 & & \
\text { Total } & 50 & 569.8262745 & & & \
\hline
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coefficients } & \text { Standard Ewor } & t \text { Stat } & \text { P-value } & \text { Lower 95\%6 } & \text { Ueper 9596 } \
\hline \text { Intercept } & 40.59256588 & 1.597069735 & 25.41690259 & 7.09161 \mathrm{E}-30 & 37.38313415 & 43.80199761 \
\text { Percent Aduhs with Bachelor's Deryee } & -0.465887223 & 0.057691105 & -8.075546932 & 1.46476 \mathrm{E}-10 & -0.581821836 & -0.34995261 \
\hline
\end{array}$

$\text { Figure } 5.2$
-Based on the Excel output in Figure 5.2,you should conclude that the estimated sample regression function is

Accepted Answer

A) statistically significant because 65.21 > .05. 
B) statistically significant because 1.465E - 10 E - 30  1.96. 
A) statistically significant because 65.21 > .05. 
B) statistically significant because 1.465E - 10 E - 30  1.96.

Question 13

What is a sampling distribution? Why is it important? Explain.

Accepted Answer

A sampling distribution is the

Question 14

What is the intuition behind the p-value method of hypothesis testing? Explain.

Accepted Answer

The p-value is the probability of observ

Question 15

Figure:
Suppose you regress U.S.annual real GDP ($ billions)on U.S.annual real defense expenditures ($ millions)and that you get the following results. SUMMARY OUTPUT

$\begin{array}{lc}
\hline \text { Regvessiait Statistics } & \
\hline \text { Muatiple R. } & 0.523337059 \
\text { R Sqare } & 0.273881677 \
\text { Adjusted R Square } & 0.263508558 \
\text { Standard Error } & 3201.551247 \
\text { Obsenvations } & 72 \
\hline
\end{array}$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & \text { of } & S S & \text { MS } & F & \text { Siguffecance } F \
\hline \text { Regressice } & 1 & 270629128.2 & 270629128.2 & 26.4030211 & 2.39636 \mathrm{E}-06 \
\text { Residual } & 70 & 717495127 & 10249930.39 & & \
\text { Total } & 71 & 988124255.3 & & & \
\hline
\end{array}
\end{array}$

$\begin{array}{lcccccc}
\hline & \text { Coeffieients } & \text { Staudard Errar } & t \text { Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper } 95 \% 6 \
\hline \text { linercept } & 1273.293919 & 979.7967762 & 1.299548998 & 0.198019186 & -680.8491085 & 3227.436946 \
\text { Real Defense Expesdtures (milions) } & 0.013659042 & 0.002658235 & 5.138387013 & 2.39636 \mathrm{E}-06 & 0.008357359 & 0.018960725 \
\hline
\end{array}$

$\text { Figure } 5.1$

-Based on the Excel output in Figure 5.1,you should conclude that the estimated sample regression function is

Accepted Answer

A) statistically significant because 2.39636E - 06  .05. 
C) statistically insignificant because 2.39636E - 06  .05. 
A) statistically significant because 2.39636E - 06  .05. 
C) statistically insignificant because 2.39636E - 06  .05.

Question 16

Why is hypothesis testing is necessary? Explain.

Accepted Answer

Because we cannot observe the true value

Question 17

A confidence interval is constructed

Accepted Answer

A) to bracket the sample mean. 
B) to bracket the sample statistic. 
C) to bracket the population parameter. 
D) to bracket the margin of error. 
A) to bracket the sample mean. 
B) to bracket the sample statistic. 
C) to bracket the population parameter. 
D) to bracket the margin of error.

Question 18

When using the critical value method for hypothesis testing,if the value of the test statistic is less than the critical value,then you should

Accepted Answer

A) reject the null hypothesis. 
B) fail to reject the null hypothesis. 
C) choose a smaller critical value that is less than the test statistic. 
D) calculate a new test statistic that exceeds the critical value. 
A) reject the null hypothesis. 
B) fail to reject the null hypothesis. 
C) choose a smaller critical value that is less than the test statistic. 
D) calculate a new test statistic that exceeds the critical value.

Question 19

If we find that it is unlikely to observe the sample statistic that is actually observed if the null hypothesis is true,then we should

Accepted Answer

A) fail to reject the null hypothesis. 
B) reject the null hypothesis. 
C) reject the alternative hypothesis. 
D) calculate a new sample statistic. 
A) fail to reject the null hypothesis. 
B) reject the null hypothesis. 
C) reject the alternative hypothesis. 
D) calculate a new sample statistic.

Question 20

A standard error is

Accepted Answer

A) the variance of the sampling distribution. 
B) the standard deviation of the population distribution. 
C) the standard deviation of the sampling distribution. 
D) the variance of the population distribution. 
A) the variance of the sampling distribution. 
B) the standard deviation of the population distribution. 
C) the standard deviation of the sampling distribution. 
D) the variance of the population distribution.

When using the p-value method for hypothesis testing,if the calculated p-value is smaller than the chosen significance level,then you should

Why are each of the individual simple linear regression model assumptions important? Explain.

A sampling distribution is

The t-statistic for the individual significance of the estimated slope coefficient $\hat { \beta } _ { 1 }$ Is

What is the intuition behind the critical-value method of hypothesis testing? Explain.

The logic behind the F-test for the overall significance of the estimated sample regression function is that if the estimated sample regression function explains a significant amount of the variation in the dependent variable,then

The logic behind the t-test for the individual significance of the estimated slope coefficient $\hat { \beta } _ { 1 }$ Is that if the estimated slope coefficient is likely to be different from 0,then

What is the intuition behind the confidence interval method of hypothesis testing? Explain.

The p-value method for hypothesis testing relies on the fact that

What is a sampling distribution? Why is it important? Explain.

What is the intuition behind the p-value method of hypothesis testing? Explain.

Why is hypothesis testing is necessary? Explain.

A confidence interval is constructed

When using the critical value method for hypothesis testing,if the value of the test statistic is less than the critical value,then you should

If we find that it is unlikely to observe the sample statistic that is actually observed if the null hypothesis is true,then we should

A standard error is

An Introduction to Econometrics and Statistical Inference

Collection and Management of Data

Summary Statistics

Simple Linear Regression

Multiple Linear Regression Analysis

Qualitative Variables and Non-Linearities in Multiple Linear Regression Analysis

Model Selection in Multiple Linear Regression Analysis

Heteroskedasticity

Time Series Analysis

Auto-Correlation

Limited Dependent Variables

Panel Data

Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Quantile Regression, Count Data, Sample Selection Bias, and Quasi-Experimental Methods

Filters

Exam 5: Hypothesis Testing in Linear Regression Analysis

When using the p-value method for hypothesis testing,if the calculated p-value is smaller than the chosen significance level,then you should

Why are each of the individual simple linear regression model assumptions important? Explain.

A sampling distribution is

The t-statistic for the individual significance of the estimated slope coefficient β^1\hat { \beta } _ { 1 }β^​1​ Is

What is the intuition behind the critical-value method of hypothesis testing? Explain.

The logic behind the F-test for the overall significance of the estimated sample regression function is that if the estimated sample regression function explains a significant amount of the variation in the dependent variable,then

The logic behind the t-test for the individual significance of the estimated slope coefficient β^1\hat { \beta } _ { 1 }β^​1​ Is that if the estimated slope coefficient is likely to be different from 0,then

What is the intuition behind the confidence interval method of hypothesis testing? Explain.

The p-value method for hypothesis testing relies on the fact that

What is a sampling distribution? Why is it important? Explain.

What is the intuition behind the p-value method of hypothesis testing? Explain.

Why is hypothesis testing is necessary? Explain.

A confidence interval is constructed

When using the critical value method for hypothesis testing,if the value of the test statistic is less than the critical value,then you should

If we find that it is unlikely to observe the sample statistic that is actually observed if the null hypothesis is true,then we should

A standard error is

An Introduction to Econometrics and Statistical Inference

Collection and Management of Data

Summary Statistics

Simple Linear Regression

Multiple Linear Regression Analysis

Qualitative Variables and Non-Linearities in Multiple Linear Regression Analysis

Model Selection in Multiple Linear Regression Analysis

Heteroskedasticity

Time Series Analysis

Auto-Correlation

Limited Dependent Variables

Panel Data

Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Quantile Regression, Count Data, Sample Selection Bias, and Quasi-Experimental Methods

Filters

The t-statistic for the individual significance of the estimated slope coefficient $\hat { \beta } _ { 1 }$ Is

The logic behind the t-test for the individual significance of the estimated slope coefficient $\hat { \beta } _ { 1 }$ Is that if the estimated slope coefficient is likely to be different from 0,then