BIA Exam 2

True or false: When predicting the value of y, given x, we use a value of 1 for the error term, ε.

False

To validate the regression assumptions, plots are often made of the residuals versus ______

the predicted values of the dependent variable, yˆŷ. the values of the independent variable, x. time.

The 100(1 - α) percent confidence interval for the slope is based on ______

the t distribution with n - 2 degrees of freedom.

When testing the significance of the y intercept, the test statistic is based on ______

the t distribution with n - 2 degrees of freedom.

The independence assumption in simple linear regression is most likely to be violated when ______ data are being used.

time series

What type of relationship exists between x and y if y tends to decrease as x increases?

negative

A simple linear regression model relating a student's SAT score, y, to the number of hours she spent studying, x, is given by y^ = 353.2 + 25.3x. Predict the SAT score for a student who spends 15 hours studying. You may assume that 15 is the experimental region

732.7

When an alternating error pattern occurs over time, this is an indication of _______.

negative autocorrelation

Which of the following are assumptions underlying simple linear regression?

At any given value of x, the population of potential error term values has a mean equal to 0. At each value of x, the population of potential error terms is normally distributed.

Which of the following are assumptions underlying simple linear regression?

At any given value of x, the population of potential error term values has mean 0. The values of the error terms are independent.

Suppose the p-value for testing H0: β1 = 0 against Ha: β1≠ 0 is equal to 0.0233. If you were to test H0: ρ = 0 against Ha: ρ ≠ 0, which of the following statements is correct?

At α = 0.025, you could claim the correlation between x and y is not zero.

Suppose the p-value for testing H0: β1 = 0 against Ha: β1≠ 0 is equal to 0.0233. If you were to test H0: ρ = 0 against Ha: ρ ≠ 0, which of the following statements is correct?

At α = 0.05, you could claim the correlation between x and y is nonzero.

When testing the significance of the slope, what are the typical competing hypotheses?

H0: β1 = 0 versus Ha: β1 ≠ 0

Suppose you have several different x variables that you can use to predict the same y. In Model 1, r =.48; in Model 2, r = -.79; in Model 3, r = 0. Which model should do the best job of predicting y?

Model 2

__ is the point estimate of the variance of the error term populations.

MSE

Suppose that the slope in a simple linear regression model is β1 = 3.52. What does this suggest about the nature of the relationship between x and y?

Positive linear relationship

Which of the following statements about the correlation coefficient, r, are true?

The closer r gets to 1, the stronger the relationship between the variables. r is always between -1 and 1

How is the least squares point estimate for the slope, b1, calculated?

SSxy/SSxx

Looking at the provided residual plot, what can we conclude?

The constant-variance assumption is violated.

Suppose that when the residuals from a simple linear regression model are plotted against x, the plot shows a curved pattern. What would this imply about about the model? Multiple choice question.

The functional form of the model is probably not correct.

If we compute a 95% prediction interval for the actual gas consumption in a week where the average hourly temperature is 30 and a 95% confidence interval for the mean consumption for all weeks where the average hourly temperature is 30, what can we say?

The intervals will have the same midpoint, but the prediction interval will be longer.

If a normal plot of residuals has a bell-shaped appearance, what can we conclude?

The normality assumption is violated.

Why is it risky to predict values of y given values of x outside the experimental region?

The relationship may not be linear for values of x outside the experimental region.

Negative autocorrelation exists when ______

negative errors tend to be followed over time by positive errors. positive errors tend to be followed over time by negative errors.

Which of the following equations is correct? Total variation + explained variation = unexplained variation Explained variation - unexplained variation = total variation Total variation - explained variation = unexplained variation

Total variation - explained variation = unexplained variation

True or false: If the functional form of a regression model is incorrect, the residual plots constructed using the model will often suggest a more appropriate model.

True

True or false: Mild departures from the regression assumptions do not hinder our ability to use a regression model to make statistical inferences.

True

True or false: The closer the coefficient of determination is to 1, the better the model is at predicting y.

True

True or false: When predicting the value of y, given x, we use a value of 0 for the error term, ε.

True

True or false: When using a least squares regression line, we should not predict a value of y unless the given value of x is in the experimental region.

True

Simple linear regression results ______ sensitive to mild departures from the underlying assumptions.

are not

A 100(1 - α) percent confidence interval for the slope is ______

[b1 ± tα/2 sb1]

Intuitively, the line that best fits plotted data will be the line that a.) minimizes SSE b.) maximizes the estimated slope c.) minimizes the mean of the residuals d.) minimizes the mean of the absolute values of the residuals

a.) minimizes SSE

Suppose that the slope in a simple linear regression model is β1 = -5.18. What does this suggest about the nature of the relationship between x and y? a.) negative linear relationship b.) positive linear relationship c.) no linear relationship

a.) negative linear relationship

A graph used to show the relationship between two variables is called a(n) a.) scatter plot b.) bell curve c.) histogram d.) ogive

a.) scatter plot

Which of the following is the least squares point estimate for the slope of the least squares line? a.) Bo b.) B1 c.) b1 d.) bo

c.) b1

In regression analysis, if the interest is on estimating the mean value of the dependent variable y, a ______ interval should be constructed.

confidence

Positive autocorrelation produces a(n) ______ error pattern over time.

cyclical

Which of the following is the least squares point estimate for the y intercept of the least squares line? a.) B1 b.) b1 c.) Bo d.) bo

d.) bo

Intuitively, the line that best fits plotted data will be the line that a.) has a slope the closest to zero b.) intersects with the most number of points c.) connects the first and last points d.) minimizes the residuals

d.) minimizes the residuals

y

dependent variable

e

error term

regression can

establish that two variables have a postive linear relationship establish that two variables have a negative linear relationship

The coefficient of determination, r2, is calculated as ______ Multiple choice question.

explained variation/total variation

If a scatter plot of y versus x reveals a circular pattern of dots, it would be appropriate to describe the relationship using simple linear regression. True or false

false

regression can establish that one variable causes a change in another variable true or false

false

When might it be reasonable to describe the relationship between x x and y using a simple linear regression. model?

if y values tend to increase in a linear fashion as x values increase If y values tend to decrease in a linear fashion as x values increase

x

independent variable

If the regression assumptions hold, the residuals should ______

look randomly distributed

The experimental region is the range of the ______.

observed values of x

What type of relationship exists between x and y if y tends to increase as x increases?

positive

Positive autocorrelation exists when ______

positive errors tend to be followed over time by positive errors. negative errors tend to be followed over time by negative errors.

In regression analysis, if the interest is on estimating an individual value of the dependent variable y, a ______ interval should be constructed.

prediction

If a linear relationship exists between x and y, we use _____ to measure the correlation of that relationship.

r

A(n) ______ displays the differences (yi - b0 - b1xi) plotted versus some criterion.

residual plot

B1

slope

If a linear relationship exists between x and y, correlation measures the ______ and the ______ of that relationship.

strength; direction

When testing the significance of the y intercept, what is the test statistic used?

t = b0/sb 0

How is the least squares point estimate for the y intercept, b0, calculated?

y - b1x

What is the equation for the simple linear regression model?

y = β0 + β1x + ε

Bo

y intercept

How do we predict the value of y, given x?

ŷ = b0 + b1x