ECO220Y1 Chapter Notes - Chapter 7: Dependent And Independent Variables, Regression Analysis, Linear Model

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 Yˆ 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 −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

. Suppose Y is related to R and S in the following nonlinear way:

Y= aRᵇSᶜ

a. How can this nonlinear equation be transformed into a linear form that can ve analyzed using multiple regression analysis.

Sixty-three observations are used to obtain the following regression results:

b. Test each estimated coefficient for statistical significance at the 5 percent level of significance. What are the exact significance levels for each of the estimated coefficients?

c. Test the overall equation for statistical significance at the 5 percent level of significance. Interpret the p-value of the F-statistic.

d. How well does this nonlinear model fit the data?

e. Using the estimated value of the intercept, compute an estimate of a.

f. If R = 200 and S = 1,500, compute the expected value of Y.

g. What is the estimated elasticity of R? Of S?