Ch13 Review

Simple linear regression involves the use of

A single numerical independent variable to predict the numerical dependent variable

How would one interpret a standard error of estimate that is equal to $65 in a simple linear regression analysis?

About 95% of the observed Y values fall within 130 of the least squares line.

The width of the confidence interval estimate for the predicted value of Y is dependent on:

All of the above

What factors determine whether or not an obtained correlation coefficient will be found to be a statistically significant?

All of the above factors help determine whether or not an observed correlation coefficient will be statistically significant

The proportion of variability in Y that is explained by the independent variable X in the regression model is known as the

Coefficient of Non-Determination

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson D statistic should be near 0.

FALSE

The Durbin-Watson D statistic is used to check the assumption of normality.

FALSE

The coefficient of determination represents the proportion of variability in X that can be explained by Y

FALSE

When using a simple regression model, it is acceptable to extrapolate the linear relationship and predict Y using values of X that are outside the range of X values used to construct the regression model

FALSE

Confidence intervals for the mean of Y are always narrower than prediction intervals for an individual Y for the same data set, X value and confidence level.

TRUE

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

TRUE

In performing a regression analysis involving two numerical variables, we are assuming the variation around the line of regression is consistent over the length of the entire regression line.

TRUE

The width of the confidence interval estimate for the average value of Y is dependent on the standard error of the estimate.

TRUE

When conducting a hypothesis test for the significance of a linear relationship, the t test for slope, and the t test for the correlation coefficient are identical.

TRUE

When the ANOVA Summary Table is examined closely, it is determined that the Regression sum of squares can never be greater than the Total sum of squares.

TRUE

The most common approach to finding the y-intercept and slope is the method of least squares. This method minimizes the sum of squared differences between

ctual Y values and the predicted Y values

If the plot of residuals is fan-shaped, which assumption is violated?

equal variance along the regression line (i.e., homoscedasticity).

To meet the assumptions for simple linear regression, what type of relationship should be observed between the residual values and values of X?

if the linear model is appropriate for the data, there should be no apparent relationship between the residual values and values of X

The Y intercept represents the:

predicted Y value when X = 0.

The statistical significance of the linear relationship between two numerical variables may be tested by

t test for the slope

A new member of the marketing team obtained a statistically significant positive correlation between automotive brand (Chrysler =1, Ford=2, General Motors=3, Honda=4, Toyota=5) and ratings of owner satisfaction (where 1= not at all satisfied, and 10 = highest level of satisfaction. What is the correct interpretation of this research finding?.

the correlation between automotive brand and owner satisfaction is not valid because automotive brand is a categorical variable but both X and Y must be numerical variables.

In the conduct of a simple linear regression analysis, what will be true of the correlation coefficient (rxy) and the slope coefficient?

the correlation coefficient and the slope coefficient must have the same sign

A residual represents which of the following?

the difference between the actual Y value and the predicted Y value for a given value of X.

The slope represents:

the estimated change in average Y per unit change in X.

The coefficient of determination tells us:

the proportion of total variation in Y that is explained by X.

The standard error of the estimate is a measure of:

the variation around the regression line.