Ban122 test 2 linear regression

Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. Y^ = 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. Y^ = 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

Regression analysis was applied between sales (in $1000) and advertising (in $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

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

In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination 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 this data is

1

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 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

If the coefficient of determination is a positive value, then the regression equation

could have either a positive or a negative slope

In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then a. there is a positive correlation between X and Y b. if X is increased, Y must also increase c. if Y is increased, X must also increase d. None of these alternatives is correct.

d. None of these alternatives is correct.

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^ = 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

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

Regression Analysis tries to answer:

how a single variable depends on other relevant variables.

A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation Y^ = 30,000 + 4 X

increase of $1 in advertising is associated with an increase of $4,000 in sales

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation Y^ = 50,000 - 8X The above equation implies that an

increase of $1 in price is associated with a decrease of $8000 in sales

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 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

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) = B0 + B1x, is known as

regression equation

The standard error is the

square root of MSE

If MSE is known, you can compute the

standard error

In a regression analysis, the error term E is a random variable with a mean or expected value of

zero

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%

If there is a very weak correlation between two variables then the coefficient of correlation must be a much larger than 1, if the correlation is positive b much smaller than 1, if the correlation is negative c any value larger than 1 d None of these alternatives is correct.

None of these alternatives is correct.

If there is a very weak correlation between two variables, then the coefficient of determination must be a. much larger than 1, if the correlation is positive b. much smaller than 1, if the correlation is negative c. much larger than one d. None of these alternatives is correct.

None of these alternatives is correct.

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 E?

The expected value of the error term is one.

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 coefficient of determination

cannot be negative

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

The error term in simple regression represents:

the vertical distance from any point to the regression line

If two variables, x and y, have a good 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