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