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True/False Questions

Circle T or F for True or False. For full credit and reward for help, please provide a written answer using complete sentences for each question.

1. T F In a simple linear regression, if the independent variable has a small variance, the estimated slope coefficient, b^, will have a large p-value.

2. T F Demographic variables are included in an estimated demand function to proxy for tastes and preferences.

3. T F The estimated intercept, ?, in any simple or multiple regression has the same units of measure as the dependent variable, yi.

4. T F A trend variable in a linear regression model will shift the intercept up or down.

5. 5. T F In a simple regression, if the correlation between the dependent and independent variables is zero, the conditional mean of the dependent variable is equal to the unconditional mean.

Thank you to anyone able to help and I hope to hear from someone as soon as they can, I am trying to figure these out to reference for my test tomorrow. I am not sure how to properly state each of the answers and truly appreciate any help that anyone can give me in trying to help me with these questions.

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Related questions

ECON 3050

Q24. The coefficient of determination (r2) is calculated as 0.49, then the correlation coefficient:

Cannot be determined without the data

Should be - 0.70 or 0.70

Should be 0.

Neither of the above

Q25. A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

To estimate the average value of Y at a specified value of X.

To predict the value of Y for an individual, given that individual's X-value.

To estimate the change in Y for a one-unit change in X.

To determine if a change in X causes a change in Y.

Q26. Which choice is not an appropriate description of Yร‹ย† in a regression equation?

Estimated response

Predicted response

Estimated average response

Observed response

Q27. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

Compute a regression line from a sample and see if the sample slope is 0.

Compute the correlation coefficient and see if it is greater than 0.5 or less than รขยˆย’0.5.

Conduct a test of the null hypothesis that the population slope is 0.

Conduct a test of the null hypothesis that the population intercept is 0.

Q28. There is no relationship between variables unless the data points lie in a straight line.

True

False

Q29. The sample regression analysis

Is the same as the population regression line

Is used to estimate the population regression line

Shows the true relation between dependent and independent variables

None of the above.

Q30. In regression, a dependent variable is sometimes called a predictor variable.

True

False

Q31. In a linear regression equation of the form y = a + bx, the intercept shows

The amount that y changes when x changes by one unit

The amount that x changes when y changes by one unit

The value of y when x is zero

The value of x when y is zero.

Q32. In a linear regression equation of y = a + bx, the slope b shows

Y / b

X / b

Y / X

X / Y

Econ 3050

7. When every member of the accessible population has an equal chance of being selected to participate in the study, the researcher is using:

a) Simple random sampling

b) Stratified random sampling

c) Convenience sampling

d) Purposive random sampling

8. A regression line has been found that has nearly all the points lying directly on the line, and only a few of them stray away from the line. Therefore, the standard error of the estimate is likely to be

Huge.

Small.

0.

Undefined.

9. Correlation coefficient ranges from _______ to ____________.

a) - 1 to 0.

b) 0 to 1.

c) -1 to 1.

d) None of the above.

10. The correlation coefficient of determination is the:

a) Ratio of the explained variation to the total deviation.

b) Ratio of the unexplained deviation to the explained deviation.

c) Ratio of the unexplained deviation to the total variation.

d) Ratio of the explained variation to the total variation.


11. If the correlation coefficient r = 0.5 then the coefficient of determination is:

a) 0.10

b) 0.25

c) 1.00

d) 2.50

12. Which one of the following is NOT appropriate for studying the relationship between two quantitative variables?

Scatterplot

Bar chart

Correlation

Regression

13. In regression, an independent variable is sometimes called a response variable.

True

False

14. The simple linear regression equation can be written y = b0 + b1x. In the simple linear regression equation, the symbol y represents:

The average or predicted response

Estimated intercept

Estimated slope

Explanatory variable

For the record, this is a homework question. A statistics student wishes to understand the relationship between a used car's price and the number of miles that car has been driven. The student goes to a local car lot and writes down the prices and the odometer reading for 100 cars. The student takes this information and completes a regression. The goal is to examine how the miles drove impacts the car's price. The regression output appears at the end of this assignment. Use the output to answer the following questions.

a) (3 points) Dependent variables Independent variable

b) (8 points) Do you expect a positive, negative, or no relationship between miles driven and price? Draw a scatterplot that corresponds to your relationship.

Be sure to include which variable (miles or price) is on the x-axis and which is on the y-axis.

b) (3 points) Write the regression equation (I want the specific estimates for the coefficients)

c) (3 points) What is the interpretation of the slope coefficient of b 1 (in terms of this problem)?

d) (4 points) Is b 1 significant from zero? How do you know?

e) (3 points) Use the regression equation to predict the price for a car that was driven for 30,000 miles. Is this mileage appropriate to make a prediction? Why or why not?

f) (3 points) Use the regression equation to predict the price for a car that was driven for 80,000 miles. Is this mileage appropriate to make a prediction? Why or why not?

g) (3 points) What percentage of price variation is explained by the variation in miles driven?

Multiple R 0.398635

R square 0.15891

Adjusted R Squared 0.150327

Standard Error 1481.414

Observations 100

df ss ms f significance f

Regression 1 40633716.14 40633716 18.51542325 3.99E-05

Residual 98 215069573.5 2194587

Total 99 255703289.7

coefficient standard error t stat p value lower 95%

intercept 20261.42 598.0313643 33.8802 6.53E-56 19074.64824

x1 -0.07332 0.017039697 -4.30296 3.99E-05 -0.107135778

Sample range for Y 14281 20511

Sample range for X 19100 49200

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