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.