Exam 10: Regression Analysis: Estimating Relationships

In a simple regression with a single explanatory variable, the multiple R is the same as the standard correlation between the Y variable and the explanatory X variable.

To help explain or predict the response variable in every regression study, we use one or more explanatory variables. These variables are also called response variables or independent variables.

The multiple R for a regression is the correlation between the observed Y values and the fitted Y values. .

In regression analysis, the variable we are trying to explain or predict is called the:

Correlation is a summary measure that indicates:

The weakness of scatterplots is that they:

The information below represents the relationship between the selling price (Y, in $1000) of a home, the square footage of the home ( ), and the number of bedrooms in the home ( ). The data represents 65 homes sold in a particular area of a city and was analyzed using simple linear regression for each independent variable. -(A) Is there evidence of a linear relationship between the selling price and the square footage of the homes? If so, interpret the least squares line and characterize the relationship (i.e., positive, negative, strong, weak, etc.). (B) Identify and interpret the coefficient of determination ( ) for the model in (A). (C) Identify and interpret the standard error of estimate for the model in (A). (D) Is there evidence of a linear relationship between the selling price and number of bedrooms of the homes? If so, interpret the least squares line and characterize the relationship (i.e., positive, negative, strong, weak, etc.). (E) Identify and interpret the coefficient of determination ( ) for the model in (D). (F) Identify and interpret the standard error of the estimate ( ) for the model in (C). (G) Which of the two variables, the square footage or the number of bedrooms, is the relationship with home selling price stronger? Justify your choice.

The correlation value ranges from:

The covariance is not used as much as the correlation because:

Given the least squares regression line, , which statement is true?

A "fan" shape in a scatterplot indicates:

A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: = 32 + 8X. This implies that an increase of $1 in advertising is expected to result in an increase of $40 in sales.

In reference to the equation, , the value 0.10 is the expected change in Y per unit change in .

A negative relationship between an explanatory variable X and a response variable Y means that as X increases, Y decreases, and vice versa.

When the scatterplot appears as a shapeless swarm of points, this can indicate that there is no relationship between the response variable Y and the explanatory variable X, or at least none worth pursuing.

Cross-sectional data are usually data gathered from approximately the same period of time from a cross-sectional of a population.

In a nonlinear transformation of data, the Y variable or the X variables may be transformed, but not both.

The regression line = 3 + 2X has been fitted to the data points (4, 14), (2, 7), and (1, 4). The sum of the residuals squared will be 8.0.

The percentage of variation ( ) can be interpreted as the fraction (or percent) of variation of the

In regression analysis, we can often use the standard error of estimate to judge which of several potential regression equations is the most useful.