Multiple Regression & Correlation & Simple linear Regression

A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds). Two variables thought to affect weight loss are client's length of time on the weight-loss program and time of session. These variables are described below: Y=Weight loss (in pounds) X subscript 1= Length of time in weight-loss program (in months) X subscript 2= 1 if morning session, 0 if not Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the interaction model : Y equals beta subscript 0 plus beta subscript 1 X subscript 1 plus beta subscript 2 X subscript 2 plus beta subscript 3 X subscript 1 X subscript 2 plus epsilon

A client on a weight-loss program

Referring to the scenario in Question 12, what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores?

Do not reject the null hypothesis; hence there is insufficient evidence to show that ACT scores and GPA are linearly related

The least squares method minimizes which of the following ?

SSE

The Variance Inflationary Factor (VIF) measures the

correlation of the X variables with each other

The Y-intercept (b subscript 0) represents the

estimated average Y when X=0

The residuals represent

the difference between the actual Y values and the predicted Y values.

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending. What should the microeconomist who developed this multiple regression model be particularly concerned with?

Collinearity

What do we mean when we say that a simple linear regression model is "statistically" useful?

The model is a better predictor of Y than the sample mean top enclose Y

Referring to the scenario in Question 9, in terms of beta s in the model, give the mean change in weight loss (Y) for every 1 month increase in time on the program (X subscript 1) when not attending the morning session

beta subscript 1

The effect of an unpredictable, rare event will be contained in the ---------- component

irregular

A dummy variable is used as an independent variable in a regression model when

the variable involved is categorical

If a categorical independent variable contains 2 categories , then how many dummy variable(s) will be needed to uniquely represent these categories ?

1

Referring to the scenario in Question 12, what is the predicted value of GPA when ACT=20?

2.61

Referring to the scenario in Question 12, the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT is

2.8633

It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the output for predicting GPA using the ACT scores based on a data set of 8 randomly chosen students from a Big-ten university The interpretation of the coefficient of determination in this regression is

ACT scores account for 57.74% of the total fluctuation in GPA

To explain personal consumption (CONS) measured in dollars, data is collected for INC: personal income in dollars CRDTLIM: $1 plus the credit limit in dollars available to the individual APR: mean annualized percentage interest rate for borrowing for the individual ADVT: per person advertising expenditure in dollars by manufacturers in the city where the individual lives SEX: gender of the individual; 1 if female, 0 if male A regression analysis was performed with CONS as the dependent variable and CRDTLIM, APR, ADVT, and GENDER as the independent variables. The estimated model was Y with hat on top equals 2.28 minus 0.29 space C R D T L I M plus 5.77 space A P R plus 2.35 A D V T plus 0.39 space S E X What is the correct interpretation for the estimated coefficient for GENDER?

Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be $0.39 higher than males

If the correlation coefficient ( r )=1.00, then

all the data points must fall exactly on a straight line with a positive slope

You need to decide whether you should invest in a particular stock. You would like to invest if the price is likely to rise in the long run. You have data on the daily mean price of this stock over the past 12 months. Your best action is to

estimate a least square trend model

In a multiple regression model, the value of the coefficient of multiple determination r squared

has to fall between 0 and +1

Referring to the scenario in Question 12, the value of the measured (observed) test statistic of the F-test for H subscript 0 : space beta subscript 1 equals 0 vs H subscript 1 : space beta subscript 1 space n o t space e q u a l space t o space 0

is always positive

The coefficient of multiple determination r squared

measures the proportion of variation in Y that is explained by X subscript 1 and X subscript 2

The Y-intercept ( b subscript 0) represents the

predicted value of Y when X=0

The fairly regular fluctuations that occur within each year would be contained in the _____ component

seasonal

Testing for the existence of correlation is equivalent to

testing for the existence of the slope (beta subscript 1)

The slope (b subscript 1) represents

the estimated average change in Y per unit change in X

In a multiple regression problem involving two independent variables, if b subscript 1 is computed to be plus 2, it means that

the estimated mean Y increases by 2 units for each increase of 1 unit of X subscript 1 , holding X subscript 2 constant

The coefficient of determination (r squared) tells you

the proportion of total variation that is explained

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals -0.3

the slope (b subscript 1) is negative

In performing a regression analysis involving two numerical variables, you are assuming

the variation around the line of regression is the same for each X value.

The method of moving averages is used

to smooth a series

The overall upward or downward pattern of the data in an annual time series will be contained in the ________ component

trend