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# Simple Linear Regression Questions

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Your company builds roads, bridges, schools and other multi-million dollar public construction projects. Competitive bids are made for the contracts to undertake these projects. For each project there are three costs:
a) the best estimate of what the project will cost your company to complete, made before a bid is submitted;
b) the "adjusted" cost on which the company bases its bid; this cost is the best estimate plus or minus a percentage which reflects how much your company wants to win the contract, and is also made before a bid is submitted;
c) on those projects for which your company is the winning bidder, the actual cost of completing the project; this is calculated after the project is completed.

You want to know whether the estimates of costs that are made prior to the bidding process are accurate predictors of the actual costs of completed projects.

Explain how you would use a simple linear regression model to answer that question. In your explanation, address the following questions:

a) How would you calculate the slope of the line?
b) How would you test the significance of the slope of the line?
c) How would you interpret the result of the test in b)?
d) Repeat a), b) and c) for the coefficient of correlation.

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#### Solution Preview

Your company builds roads, bridges, schools and other multi-million dollar public construction projects. Competitive bids are made for the contracts to undertake these projects. For each project there are three costs:

a) the best estimate of what the project will cost your company to complete, made before a bid is submitted;
b) the "adjusted" cost on which the company bases its bid; this cost is the best estimate plus or minus a percentage which reflects how much your company wants to win the contract, and is also made before a bid is submitted;
c) on those projects for which your company is the winning bidder, the actual cost of completing the project; this is calculated after the project is completed.

You want to know whether the estimates of costs that are made prior to the bidding process are accurate predictors of the actual costs of completed projects.

Explain how you would use a simple linear regression model to answer that question. In your explanation, address the following questions:

You would make a regression model using the actual cost as the dependent (y) variable and either the estimate or adjusted estimate as the independent (x) variable. It is possible to make a regression model with two independent variables (so you could use the estimate and the adjusted ...

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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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