Simple Linear Regression Flashcards
A numerical measure of linear association between two variables is the
covariance
A numerical measure of linear association between two variables is the
correlation coefficient
The coefficient of correlation
cannot be larger than 1
In a regression analysis, the error term is a random variable with a mean or expected value of
zero
The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = 0 + 1x, is known as
regression equation
A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation
Y hat= 30,000 + 4 X
increase of $1 in advertising is associated with an increase of $4,000 in sales
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.
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
the regression model
In a 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
Y hat = 60 - 8X
The above equation implies that an
increase of $1 in price is associated with a decrease of $8000 in sales
A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation
Y8 = 9 - 3X
The above equation implies that if the price is increased by $1, the demand is expected to
decrease by 3,000 units
A least squares regression line
may be used to predict a value of y if the corresponding x value is given
The coefficient of determination
cannot be negative
The value of the coefficient of correlation (R)
can be equal to the value of the coefficient of determination (R2)
In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is
0.65
Correlation analysis is used to determine
the strength of the relationship between the dependent and the independent variables
In a regression and correlation analysis if r squared = 1, then
SSR = SST
In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is
0.6000
If the coefficient of correlation is a positive value, then the regression equation
must have a positive slope
In regression and correlation analysis, if SSE and SST are known, then with this information the
coefficient of determination can be computed
SSE can never be
larger than SST
If the coefficient of correlation is a negative value, then the coefficient of determination
must be positive
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
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
In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is
0.40
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 correlation is 0.90, then the coefficient of determination
must be 0.81
If the coefficient of correlation is a positive value, then
the slope of the line must be positive
In regression analysis, which of the following is not a required assumption about the error term (backward 3)
The expected value of the error term is one.
In regression analysis, the unbiased estimate of the variance is
mean square error
If only MSE is known, you can compute the
standard error
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.
The interval estimate of the mean value of y for a given value of x is
confidence interval estimate
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.
Y hat = 120 - 10 X
Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to
decease by 20 units
Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained.
Y hat = 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
Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained.
Y hat = 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
