Stats
If the coefficient of determination is 0.81, the coefficient of correlation
None of these answers is correct.
In regression analysis if the dependent variable is measured in dollars, the independent 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
In simple linear regression, r2 is the
coefficient of determination
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
SSE can never be
larger than SST
Larger values of r2 imply that the observations are more closely grouped about the
least squares line
If there is a very strong correlation between two variables, then the coefficient of correlation must be
can be either -1 or +1
The numerical value of the coefficient of determination
can be larger or smaller than the coefficient of correlation
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
simple linear regression EQUATION
y(hat)= Bo + B1x
Simple linear regression model
y= Bo + B1x + E
A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is the
least squares method
It is possible for the coefficient of determination to be
less than one
A data point (observation) that does not fit the trend shown by the remaining data is called a (an)
narrower
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
In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is
0.6000
In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is
0.65
Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function 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 if SSE = 500 and SSR = 300, then the coefficient of determination is
.3750
If a data set has SST = 2,000 and SSE = 800, then the coefficient of determination is
.6
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 this data is
1
Assumptions About Error Term E
1. Error E is a random variable with mean of zero 2. The Variance of E, denoted by sigma^2, is the same for all values of E are independent 3. The values of E are independent 4. The error E is a normally distributed random variable
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 results.
In regression analysis, which of the following is not a required assumption about the error term ε?
All are required assumptions about the error term.
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 answers is correct.
In a regression analysis if r2 = 1, then
SSE must be equal to zero
In a regression analysis if r2 = 1, then
SSR = SST
Which of the following is correct?
SST = SSR + SSE
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
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the
coefficient of determination
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 the
confidence interval
A measure of the strength of the relationship between two variables is the
correlation coefficient
If the coefficient of determination is a positive value, then the regression equation
could have either a positive or a negative slope
In regression analysis, the variable that is being predicted is the
dependent variable
A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation = 50,000 + 6x The above equation implies that an
increase of $1 in advertising is associated with an increase of $6,000 in sales
A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 50,000 − 8x
increase of $1 in price is associated with a decrease of $8000 in sales
An observation that has a strong effect on the regression results is called a (an)
influential observation
If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the estimated regression equation
is 16%
In a regression analysis, the variable that is being predicted
is the dependent variable
A least squares regression line
may be used to predict a value of y if the corresponding x value is given
The least squares criterion is
min
If the coefficient of correlation is a positive value, then the slope of the regression line
must also be positive
If the coefficient of correlation is a negative value, then the coefficient of determination
must be positive
Application of the least squares method results in values of the y intercept and the slope that minimizes the sum of the squared deviations between the
observed values of the dependent variable and the predicted values of the dependent variable
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 difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the
residual
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
the regression model
As the goodness of fit for the estimated regression equation increases
the value of the coefficient of determination increases
