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Multiple Choice questions on least squares estimation

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Answer this question (question 17) and questions 18 and 19 on the basis of the following regression results, standard errors in parentheses, n = 200)

Qd = -500 - 100Pa + 50Pb + .3I + .2A
(250) (50) (30) (.1) (.08)

R2 = .12
Where Qd = 10,500 quantity demanded of product "A"
Pa = $10, price of product "A"
Pb = $8, price of product "B"
I = $12,000 per capita income
A = $20,000 monthly advertising expenditure

1. Which of the Variables does NOT pass the t-test at the .05 level of significance?

a. Pa
b. Pb
c. A
d. I
e. All the variables pass the t-test

2. As a researcher, which aspect of the results would be of greatest concern?

a. The negative value of the constant (i.e., -500)
b. The relatively low impact of the competitor's price
c. The fact that not all of the variables are statistically significant
d. The poor fit of the regression line

3. As the manager of Product A, which of the following would be of greatest concern (based on the regression results above)?

a. None of the factors below would be of concern.
b. An impending recession.
c. Pressure on you by your salespersons to lower the price so that they can boost their sales.
d. A price reduction by the makers of product B.

4. Among the advantages of the least-squares trend analysis techniques is

a. The ease of calculation.
b. Relatively little analytical skill required.
c. Its ability to provide information regarding the statistical significance of the results.
d. All of the above

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Solution Summary

The solution gives answers to multiple choice questions on least squares estimation. The questions are related to regression equation, Student's t-test, least squares estimation, slope, intercept, correlation, residual, R square, coefficient of determination and regression coefficients.

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20 Linear Regression Multiple Choice Questions

In a regression analysis, the error term ? is a random variable with a mean or expected value of

zero

one

any positive value

any value

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

the correlation model

the regression model

correlation analysis

None of these alternatives is correct.

For a given value of x, the estimation interval for an individual y observation is called the:

confidence interval.

residual.

prediction interval.

least-squares interval.

standard error of estimate.

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: y hat = 75 +6x. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is:

$4875.

$123,000.

$487,500.

$12,300.

A least squares regression line

may be used to predict a value of y if the corresponding x value is given

implies a cause-effect relationship between x and y

can only be determined if a good linear relationship exists between x and y

None of these alternatives is correct.

The value for SSE equals zero. This means that the coefficient of determination (r^2) must equal:

0.0.

-1.0.

2.3.

-2.3.

1.0.

Which of the following statements is true regarding the simple linear regression model y sub i = beta sub 0 + beta sub 1 * x sub i + epsilon sub i:

y sub i is a value of the dependent variable (y) and x sub i is a value of the independent variable (x)

beta sub 0 is the y-intercept of the regression line.

beta sub 1 is the slope of the regression line.

epsion i is a random error, or residual.

All of the above are true statements.

Correlation analysis is used to determine the:

strength of the relationship between x and y.

least squares estimates of the regression parameters.

predicted value of y for a given value of x.

coefficient of determination.

An indication of no linear relationship between two variables would be:

a coefficient of determination equal to 1.

a coefficient of determination equal to -1.

a coefficient of correlation of 0.

a coefficient of correlation equal to -1.

Both "A" and "B" are correct.

Given the least squares regression line y hat = -2.88 + 1.77x, and a coefficient of determination of 0.81, the coefficient of correlation is:

-0.88.

+0.88.

+0.90.

-0.90.

The residual is defined as the difference between the:

actual value of y and the estimated value of y.

actual value of x and the estimated value of x

actual value of y and the estimated value of x.

actual value of x and the estimated value of y.

Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained.
= 120 - 10 X
Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

increase by 120 units

increase by 100 units

increase by 20 units

decease by 20 units

Simple linear regression requires that the scales of measurement be expressed in either:

nominal or ordinal.

ordinal or ratio.

interval or ratio.

nominal or ratio.

nominal or interval.

If the coefficient of correlation is a positive value, then the regression equation

must have a positive slope

must have a negative slope

could have either a positive or a negative slope

must have a positive y intercept

Correlation analysis is used to determine

the equation of the regression line

the strength of the relationship between the dependent and the independent variables

a specific value of the dependent variable for a given value of the independent variable

None of these alternatives is correct.

In order to estimate with 95% confidence the expected value of y in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

2.228

2.306

1.860

1.812

If the sum of squares due to regression (SSR) is 60, which of the following must be true?

The coefficient of correlation is 0.9.

The total sum of squares (SST) is at least 60.

The y-intercept is positive.

The slope, b, is positive.

The coefficient of determination is 0.81.

In regression and correlation analysis, if SSE and SST are known, then with this information the

coefficient of determination can be computed

slope of the line can be computed

Y intercept can be computed

x intercept can be computed

The regression line y hat = 3 + 2x has been fitted to the data points (4,8), (2,5), and (1,2). The residual sum of squares will be:

10.

15.

13.

22.

The vertical spread of the data points about the regression line is measured by the:

regression coefficient.

standard error of estimate.

y-intercept.

homoscedasticity coefficient.

t-ratio.

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