Stats Quiz #2

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.

decease by 20 units.

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: ​ = 9 - 3x

decrease by 3000 units.

Larger values of r2 imply that the observations are more closely grouped about the

least squares line.

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see​ a

horizontal band of points centered near zero.

coefficient of determination

a measure of the amount of variation in the dependent variable about its mean that is explained by the regression equation

If the coefficient of determination is equal to 1, then the coefficient of correlation

can be either -1 or +1.

positive coefficient determination, coefficient correlation is ...

can be either positive or negative

All the independent variables in a multiple regression analysis

can be either quantitative or qualitative or both.

The value of the coefficient of correlation (r)

can be equal to the value of the coefficient of determination (r2).

If the coefficient of correlation is a positive value, then the

slope of the regression line must be positive.

coefficient of correlation

square root of the r-square

confidence interval estimate

the interval estimate of the mean value of y for a given value of x

In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then

the estimated regression line intercepts the positive y-axis

In regression analysis, the independent variable is

used to predict the dependent variable.

regression equation

y=a+bx

. A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: ​ = 30,000 + 4x

increase of $1 in advertising is associated with an increase of $4000 in sales.

= b0 + b1x,

b1 is slope

Regression analysis was applied between sales (y in $1000) and advertising (x in $100) and the following estimated regression equation was obtained. ​ = 80 + 6.2x

$700,000.

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4x

$900,000.

In a regression analysis, the coefficient of correlation is .16. The coefficient of determination in this situation is

.0256.

. In a regression analysis, the coefficient of determination is .4225. The coefficient of correlation in this situation is

.65 if b1 is positive.

. If the coefficient of determination is .90, the percentage of variation in the dependent variable explained by the variation in the independent variable is

.81%.

error term has a mean of

0

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

64%.

estimated regression equation

The estimate of the regression equation developed from sample data by using the least squares method.

prediction interval estimate

The interval estimate of an individual value of y for a given value of x is the

In regression analysis, if the dependent variable is measured in dollars, the independent variable

can be measured in any units.

In regression analysis, if the independent variable is measured in pounds, the dependent variable

can be measured in any units.

A least squares regression line

can be used to predict a value of y if the corresponding x value is given.

If there is a very weak correlation between two variables, then the coefficient of determination must be

closer or equal to zero.

What is R squared?

coefficient of determination

A descriptive measure of the strength of linear association between two variables is the​

correlation coefficient.

In regression analysis, the variable that is being predicted is the

dependent variable.

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: ​ = 60 - 8x

increase of $1 in price is associated with a decrease of $8000 in sales.

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data

is 1.

If the coefficient of correlation is -.4, then the slope of the regression line

must be negative.

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

one dependent and one or more independent variables are related.

. The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as the

regression equation

In regression analysis, the model in the form y = + x + ε is called the

regression model

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

the regression model.

Correlation analysis is used to determine

the strength of the linear relationship between the dependent and the independent variables.