Exam 2 Stat Meth Bus

Using the best-subsets approach to model building, models are being considered when their

Cp <= k+1

Which of the following is used to find a "best" (most appropriate) model?

Cp statistic or adjusted R square

Choose variables based on VIFj values. For a dataset with 4 independent variable, VIF1=1.54, VIF2=5.54, VIF3=7.89, VIF4=6.90, we should

DELETE X3

In a multiple regression model, which of the following is correct regarding the value of the adjusted r^2

It has to be positive.

The least squares method minimizes which of the following?

SSE

Which of the following statements about linear regression is incorrect?

SSR measures unexplained variation.

D Message 1 https://cdn.discordapp.com/attachments/883501430177148949/1043402912103153695/image.png

The predicted Asking Price of House Type ranch is 81.94 more expensive than the predicted Asking Price of House Type other holding Living Space and Fireplace constant.

D 2 https://cdn.discordapp.com/attachments/883501430177148949/1043403395328917574/image.png

There is insufficient evidence (at α = 0.05) to indicate that the relationship between weight loss (Y) and months on program(X1) varies with session time.

SEXgender of the individual; 1 if female, 0 if male Y_hat= .....+0.39SEX What is the correct interpretation for the estimated coefficient for SEX?

females is estimated to be $0.39 higher than males. who ever has 1 = higher (if negative lower)

In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that

the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant.

An interaction term in a multiple regression model may be used when

the relationship between X1 and Y changes for differing values of X2.

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals - 0.30,

the slope (b1) is negative.

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

the variable involved is categorical.

The plot residuals versus the predicted value of Y can be used to discover a possible curvilinear effect in at least one independent variable.

True

The standard error of the estimate, SYX, measures the variability of the observed Y values from the predicted ones.

True

The Variance Inflationary Factor (VIF) measures the

correlation of the X variables with each other

The intercept (b0) represents the

predicted value of Y when X = 0.

The logarithm transformation can be used

to change a nonlinear model into a linear model.

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and constructed the multiple regression model. The business literature involving human capital shows that education influences an individual's annual income. Combined, these may influence family size. With this in mind, what should the real estate builder be particularly concerned with when analyzing the multiple regression model?

Collinearity

The Durbin-Watson D statistic is used to check the assumption of normality.

False

The Regression Sum of Squares (SSR) can be greater than the Total Sum of Squares (SST).

False

The confidence interval for the mean of Y does not depend on the value of independent variable Xi.

False

To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term.

False (Dummy Variable)

Stepwise regression approach evaluates all possible regression models.

False Stepwise regression does not fit all models but instead assesses the statistical significance of the variables one at a time and arrives at a single model.

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

True

If the correlation coefficient (r) = 1.00, then all the data points must fall exactly on a straight line with a positive slope.

True

The confidence interval for the mean of Y is always narrower than the prediction interval for an individual response Y given the same data set, X value, and confidence level.

True

The strength of the relationship between two numerical variables can be measured using the correlation coefficient, r.

True

Which of the following is NOT an approach for handling nonlinear relationship between Y and X? Variance inflationary factor Square-root transformation Quadratic regression model Logarithmic transformation

Variance inflationary factor

A regression diagnostic tool used to study the possible effects of collinearity is

the VIF.

The residuals represent

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