Statistics Chapter 3

A real estate agent says he can approximate the value of a house through the following equation: SP = 125,000 + 3000BR + 500BDR + 4000WC -6000P; where BR= # of bathrooms, BDR= # bedrooms, WC =Wine cellar and P=Pool. The best selling price estimate for a 3 bedroom, 2 bath house with a wine cellar and pool is

$130,500

If you have a coefficient of determination of .049, in simple regression, what is the coefficient of correlation?

+ or - 7. The coeffient of correlation can be either negative of positive root of the coefficent of determination.

A regression line for a certain set of data is found to be y=14+9x. The mean or y or y bar is 27. A particular point os 2, 40. What is the total variation in this point.

13. The total variation is the difference between y(40) and y bar, 27, or 40-27=13.

A real estate agent says he can approximate the value of a house through the following equation: SP = 125,000 + 3000BR + 500BDR + 4000WC -6000P; where BR= # of bathrooms, BDR= # bedrooms, WC =Wine cellar and P=Pool. There are _____ zero-one variables in this regression model.

2

An independent variable has a coefficient of 2.9 and a standard deviation of 0.8. What is the T-ratio, given to the third decimal place?

3.625

Susan wants to study the effect of water on the growth of flowers in her garden. She determines a regression line where water is the independent variable (measured in fluid ounces) and flower growth is the dependent variable (measured in centimeters), If one of her flowers is 40 centimeters tall, and the regression line is y=15 + 5x, estimate how many fluid ounces of water is has been given.

5 fluid ounces.

A regression model has the equation: y=7x(v1) + 4x(v2)+9x(v3) +17 with 75 obeservations. How many degrees of freedom are in this model?

71. Take the number of observations (75) and subtract 1 plus hthe number of independent variables in your model (3) so: 75-(1+3)=71

0.00 points out of 1.00 Not flaggedFlag question Question text Let us imagine that the number of automobile accidents in a certain region are related to the regional number of registered automobiles in tens of thousands (b1), alcoholic beverage sales in $10,000 (b2), and decrease in the price of gasoline in cents (b3). Furthermore, imagine that the regression formula has been calculated as: Y = a + b1X1 + b2X2 + b3X3 where Y = the number of automobile accidents, a = 7.5, b1 = 3.5, b2 = 4.5, and b3 = 2.5 Calculate the expected number of automobile accidents for a football weekend if the region has 25,000 registered vehicles, $75,000 worth of beer is sold, and a gas war causes a 10 cent drop in a gallon of gas.

75

Which of the following tells us how much variation in the data can be explained by the regression model? Select one: a. degrees of freedom b. t statistics c. coefficient of determination d. none of the above

C. Coefficient of determination

Edna's T-ratio is less than 2 for the constant term in her regression equation. She should be A. Concerned B. Very Concerned C. Not Very Concerned D. None of the Above

C. Not very concerned. T statistics less than 2 are an area of concern for the coefficient of the independent variable because they may indicate a 0 coefficient. A 0 coefficient means there is no relationship between the independent variable and the dependent variables. On the other hand, the constant term has no particular significance to the analyst and can enjoy a low T-ratio.

Jack owns a cattle ranch in Wyoming. He wants to find out what determines how much cattle weigh. He has four factors which we believes may contribute . Which of the following should be treated as a dummy (or zero-one) variable? A.) Amount of feed eaten per day B.) Amount of time let out in the pasture C.) Steer or not D.) Age

C. Steer or not This is the only answer that can only be a yes or no answer (0 or 1) so a dummy variable must be used

Tells us how much variation in the data can be explained by the regression model we have built.

Coefficient of determination

the square root of the coefficient of multiple determination

Coefficient of multiple correlation

Shows the amount of variability in the dependent variable that is explained by both independent variables working together

Coefficient of multiple determination

T/F A correlation coefficient of -2 means that as s goes up, so does y.

FALSE. A negative correlation coefficient means that as x rises, y goes down, and vice versa. Also, the -2 is not a possible value for the correlation coefficient.

T/F In multiple regression, all independent variables are independent, i.e. they do not interact with one another.

FALSE. Generally speaking, there are always some interactions amongst the independent variables. Do not expect a computer printout to show no correlation among independent variables.

Suppose we were trying to study the effect of rain on attendance at the local Shakespeare in the Park presentation. Would rain be the independent or dependent variable??

Rain is the independent variable. Attendance is DEPENDENT on the rain since it depends of whether it rains or not.

It tells you how many standard deviations away from zero the coefficient of your independent variable is

T Ratio

T/F A regression equation can have a negative coefficient of correlation, but a positive coefficient of determination.

TRUE.

T/F f the resultant ratio from regression equation is between plus and minus 2 (or a different value established by an experienced forecaster), it is possible that the value of the coefficient is actually zero and the usefulness of the independent variable should be questioned.

TRUE.

T/F A low T-ratio for the coefficient of an idependent variable is a concern because it indicates the coefficient may be 0 or close to 0.

TRUE. The T-Ratio measures the number of standard deviations from 0 of the coefficient of the independent variable. Many analysts use 2 as the magic number. If the T Ratio is less than 2, it indicates that the coefficients may be 0 and there is no relationship between the independent variable and the dependent variable.

T/F A simple regression involves a single independent variable.

True

T/F R^2 tells us how much of the scatter of data points is explained by the regression model

True

Regression Formula:

Y'=a+bX

Which of the following is a dummy variable? Select one: a. shoe color(black or brown) b. shoe size c. shoe weight d. none of the above

a. Shoe Color (black or brown)

A positive correlation association means that

as x increases, so does y, and vice versa

A coefficient of determination of 0.94 for a regression analysis would indicate Select one: a. 6% of the variation is explained by the regression equation b. 94 % of the variation is not explained by the regression equation c. 94% of the variation is explained by the regression equation d. 6% of the variation is random

c. 94% of the variation is explained by the regression equation

Which of the following is a dummy variable? Select one: a. fish weight b. fish length c. fish species (trout or cobia) d. None of these make sense

c. Fish Species

Explained variation / total variation

coefficient of determination

Measures the degree of linear association between x and y.

correlation coefficient

A real estate agent says he can approximate the value of a house through the following equation: SP = 125,000 + 3000BR + 500BDR + 4000WC -6000P; where BDR=# bedrooms, WC =Wine cellar and P=Pool. If the owners of the house with a pool want to increase its value by the most possible they should a. add a bathroom. b. add a bedroom. c. add a wine cellar. d. fill in the pool. e. Cannot tell without more analysis

d. fill in the pool.

Found by subtracting one plus the number of independent variables from the number of observations

degrees of freedom

A regression analysis using the Y'=a+bX equation is called _______ because it assumes a straight-line relationship between X and Y

linear

A regression analysis involving two or more independent variables is called a

multiple regression

A zero-one, or dummy, variable in regression analysis is useful in regression analysis when you would like to put an important independent variable into the model which cannot be given a

numerical value

With ____________________, the forecaster is not limited to predicting the unknown variable solely from historical levels of that same variable, but is able to predict it based on one or a number of other conditions as well

regression

can be extremely accurate because it allows the forecaster to customize a prediction based on the conditions that exist, granted those conditions have existed at some point in the past so their effect on the predicted variable can be analyzed

regression analysis

Difference between the actual value and the predicted value of a dependent variable

residual

A regression analysis involving a ____________ is further classified as a simple regression

single independent variable

the measure of variation around the mean

standard deviation

the measure of variation of points around the regression line

standard error

What does r^2 stand for?

the coefficient of determination

Two ways to measure the strength of a relationship between dependent and independent variables

the coefficient of determination and the coefficient of correlation

The difference between the Y- value of a data point and the predicted value corresponding to it on the regression line

the residual

In computational terms, regression analysis is very closely related to __________

trend analysis

The coefficient of correlation (r) would tell us

which way y would change (increase or decrease) as x changes