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# Multiple choice: Confidence interval, multiple regression...

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1. Suppose that a 95% confidence interval for the population slope from a multiple regression is 0.14 to 1.33. How would we interpret this interval?
A) There is a 95% probability that the interval 0.14 to 1.33 includes the true mean.
B) 95% of the population slopes fall between 0.14 and 1.33.
C) 95% of the time the population slope falls between 0.14 and 1.33.
D) 95% of the y values fall between 0.14 and 1.33.

A) The number of predictors only.
B) The sample size only.
C) The number of predictors and the sample size.
D) None of the above

THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A real estate appraiser is interested in determining the factors that determine the price of a house. She wants to run the following regression: where Y = price of the house in \$1,000s, = number of bedrooms, = square footage of living space, and = number of miles from the beach. Taking a sample of 30 houses, the appraiser runs a multiple regression and get the following results: , = 103.2, = 2.13, = 0.062, = 4.17, , and (adjusted).

3. What price would we expect to pay on a 3 bedroom, 1,000 square foot house three miles from the beach?
A) \$201,422
B) \$177,243
C) \$243,850
D) \$229,198

4. What is the correct interpretation of the coefficient of determination ?
A) Approximately 47% of the time, sales price can be explained by these three variables.
B) Approximately 47% of the variation in sales prices can be determined by variation in these three variables.
C) The sales price equals 47% of these three variables.
D) Approximately 47% of the time, the sample values will lie on the regression line.

THE NEXT TWO QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A loan officer is interested in examining the determinants of the total dollar value of residential loans made during a month. She used to model the relationship, where Y is the total dollar value of residential loans in a month (in millions of dollars), is the number of loans, is the interest rate, and is the dollar value of expenditures of the bank on advertising (in advertising of dollars). Using data from the past 24 months, she obtained the following results: , = 3.2, = 0.03, = 0.062, = 0.17, = 0.46, and adjusted = 0.41.

5. How should she interpret the coefficient on ?
A) For every additional 1.3 percent increase in the interest rate, we would expect \$1.0 million less in loans; total dollar values, with all other independent variables in the model held constant.
B) For every additional one percent increase in the interest rate, we would expect \$1.3 million less in loans; total dollar values, with all other independent variables in the model held constant.
C) For every additional \$1.0 million in loans, we would expect the interest rate to decrease by 1.3 percent; total dollar values, with all other independent variables in the model held constant.
D) For every additional \$1.3 million in loans; total dollar values, with all other independent variables in the model held constant we would expect the interest rate to decrease by 1.0 percent.

6. What would we expect the total dollar value of loans to be in a month where there are 42 loans, the interest rate is 7.5%, and the bank spends \$30,000 in advertising?
A) \$6.442 million
B) \$6.558 million
C) \$6.288 million
D) \$6.112 million

7. A goodness -of -fit-test is to be performed to see if consumers prefer any of four package designs (A, B, C, and D) more than the other three. If a random sample of 60 consumers is selected, what is the expected frequency for category A?
A) 0.25
B) 30
C) 15
D) 10

8. For a chi-square goodness- of- fit-test, the calculated chi-square value is 7.21. If the table chi-square value is 10.645, what is the appropriate decision for this test?
A) reject the null hypothesis
B) fail to reject the null hypothesis
C) accept the alternative hypothesis
D) impossible to determine from this information

9. Consider the following data set: 16, 16, 17, 18, 20, 21, 21, 22, 23, 24, 25, 27, 27, 27, 27, and 30. The rank assigned to the four observations of value 27 is:
A) 13
B) 13.5
C) 12
D) 12.5

10. The Wilcoxon rank sum test statistic T is approximately normally distributed whenever the sample sizes are larger than:
A) 10
B) 15
C) 20
D) 25

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#### Solution Summary

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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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