business stat
Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. = 50 + 8 X Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is
$1,300,000
Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained. = 80 + 6.2 X Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is
$700,000
$100) and the following regression function was obtained. = 500 + 4 X Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is
$900,000
In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is
-0.7
regression analysis, the coefficient of correlation is 0.16. The coefficient of determination in this situation is
0.0256
In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is
0.40
In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is
0.6000
If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is
64%
A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation = 30,000 + 4 X The above equation implies that an
increase of $1 in advertising is associated with an increase of $4,000 in sales
In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is
0.65
In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is
0.65
If a data set has SSR = 400 and SSE = 100, then the coefficient of determination is
0.80
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 there is a very strong correlation between two variables then the coefficient of determination must be
None of these alternatives is correct.
If there is a very weak correlation between two variables, then the coefficient of determination must be
None of these alternatives is correct.
In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then
None of these alternatives is correct.
In a regression and correlation analysis if r2 = 1, then
SSE must be equal to zero
In a regression and correlation analysis if r2 = 1, then
SSR = SST
In simple linear regression analysis, which of the following is not true?
The F test and the t test may or may not yield the same conclusion.
In regression analysis, which of the following is not a required assumption about the error term ε?
The expected value of the error term is one.
In the following estimated regression equation
b1 is the slope
In regression analysis if the dependent variable is measured in dollars, the independent variable
can be any units
In regression analysis, if the independent variable is measured in pounds, the dependent variable
can be any units
If the coefficient of determination is equal to 1, then the coefficient of correlation
can be either -1 or +1
If the coefficient of determination is a positive value, then the coefficient of correlation
can be either negative or positive
The value of the coefficient of correlation (R)
can be equal to the value of the coefficient of determination (R2)
The coefficient of determination
cannot be negative
In regression and correlation analysis, if SSE and SST are known, then with this information the
coefficient of determination can be computed
The interval estimate of the mean value of y for a given value of x is
confidence interval estimate
If the coefficient of determination is 0.81, the coefficient of correlation
could be either + 0.9 or - 0.9
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. = 120 - 10 X
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 The above equation implies that if the price is increased by $1, the demand is expected to
decrease by 3,000 units
In regression analysis, the variable that is being predicted is the
dependent variable
The model developed from sample data that has the form of is known as
estimated regression equation
A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 60 - 8X The above equation implies that an
increase of $1 in price is associated with a decrease of $8000 in sales
In a regression analysis the standard error is determined to be 4. In this situation the MSE
is 16
If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the variation in the independent variable
is 16%.
If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable
is 90%.
In a regression analysis, the variable that is being predicted
is the dependent variable
The coefficient of correlation
is the square root of the coefficient of determination
SSE can never be
larger than SST
Larger values of r2 imply that the observations are more closely grouped about the
least squares line
It is possible for the coefficient of determination to be
less than one
A least squares regression line
may be used to predict a value of y if the corresponding x value is given
In regression analysis, the unbiased estimate of the variance is
mean square error
If the coefficient of correlation is 0.90, then the coefficient of determination
must be 0.81
If the coefficient of correlation is -0.4, then the slope of the regression line
must be negative
If the coefficient of correlation is a negative value, then the coefficient of determination
must be positive
If the coefficient of correlation is a positive value, then the regression equation
must have a positive slope
Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be
narrower
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 interval estimate of an individual value of y for a given value of x is
prediction interval estimate
The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as
regression equation
In regression analysis, the model in the form is called
regression model
The standard error is the
square root of MSE
If only MSE is known, you can compute the
standard error
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
the regression model
If the coefficient of correlation is a positive value, then
the slope of the line must be positive
Correlation analysis is used to determine
the strength of the relationship between the dependent and the independent variables
If two variables, x and y, have a strong linear relationship, then
there may or may not be any causal relationship between x and y
In regression analysis, the independent variable is
used to predict the dependent variable
In a regression analysis, the error term ε is a random variable with a mean or expected value of
zero
