Exam 14: Linear Correlation and Simple Linear Regression Analysis

The coefficient of determination is the proportion of variability of the dependent variable (y) accounted for or explained by the independent variable (x).

Consider the following scatter plot and regression line. At x = 50, the residual (error term) is ___.

Prediction intervals get narrower as we extrapolate outside the range of the data.

Annie Mikhail, market analyst for a national company specializing in historic city tours, is analyzing the relationship between the sales revenue from historic city tours and the size of the city. She gathers data from six cities in which the tours are offered. Annie's dependent variable is annual sales revenues and her independent variable is the city population. Regression analysis of the data yielded the following tables: For a city with a population of 500,000, Annie's model predicts annual sales of ___.

One of the assumptions made in simple regression is that ___.

A manager wishes to predict the annual cost (y) of an automobile based on the number of miles (x) driven. The following model was developed: y = 2,000 + 0.42x. If a car is driven 20,000 miles, the predicted cost is ___.

The standard error of the estimate, denoted s_e, is the square root of the sum of the squares of the vertical distances between the actual y values and the predicted values of y.

The following residuals plot indicates ___.

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx = 89.333, and S_e = 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The critical t value is ___.

A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. The dependent variable is ___.