Stat Exam

heteroscedasticity

the error variances are not constant

t-test

used to determine whether the coefficients of the regression model are significantly different from zero

f-test

used to determine whether the overall regression model is significant

in a regression analysis is SST = 400 and SSR = 100, r^2 = ___.

0.25

assumptions of simple regression analysis

1. the model is linear 2. the error terms have constant variances 3. the error terms are independent 4. the error terms are normally distributed

the least squares method minimizes which of the following?

SSE

correlation

a measure of the degree of relatedness of variables

r

a measure of the linear correlation of two variables. it is a number that ranges from -1 to 0 to +1, representing the strength of the relationship

confidence interval

an estimate of the average value of y for a given x, denoted E(Yx)-the expected value of y

in simple regression analysis the error terms are

assumed to be independent and normally distributed with zero mean and constant variance

nonconstant error variance

cone shaped residual plot, associated with either heteroscedasticity or homoscedasticity. the error variance is greater for small values of x and smaller for large values of x

if the plot of the residuals is cone shaped, which assumption is violated?

constant variance/homoscedesticity

a quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. production runs are done 10 hours a day, 7 days a week. the explanatory variable is ___

day of week

standard error of the estimate

denoted Se, is a standard deviation of the error of the regression model and has more practical use than SSE

residual

each difference between the actual y values and the predicted y values is the error of the regression line at a given point, y - y^

prediction interval

estimates a single value of y for a given value of x

a fruit stand owner develops a regression line, y=30 + 3x to predict y = sales amount per day ($100s), using x = the number of visitor per day (10s). the slope of this regression line suggests this: ____.

for every 10 additional visitors per day, on average, the sales amount is predicted to increase by 300 dollars

response variable

in multiple regression analysis, this is the dependent variable, y

if the correlation coefficient between two variables is 0

it means no linear relationship is present between the two variables

if the correlation coefficient between two variables is -1

it means the two variables have a perfect negative correlation

nonlinear residual plot

parabolic, not linear residual plot.

healthy residual graph

plot is relatively linear; the variances of the errors are about equal for each value of x

Pearson product-moment correlation coefficient, or coefficient of correlation

r

multiple regression

regression analysis with two or more independent variables or with at least one nonlinear predictor

partial regression coefficient

represents the increase that will occur in the value of y from a one unit increase in that independent variable if all other variables are held constant, Bi

nonindependent error terms residual plot

slanted plots, as the value of the residual is a function of the residual value net to it. a small negative residual is next to a small negative residual

the total of the squared residuals is called the

sum of squares error

homoscedasticity

the assumption of constant error variance

independent variable

the explanatory variable, designated as x

simple regression (bivariate regression)

the most elementary regression model that involves two variables in which one variable is predicted by another variable

regression analysis

the process of constructing a mathematical model or function that can be used to predict or determine one variable by another variable or other variables

coefficient of determination

the proportion of variability of the dependent variable (y) accounted for or explained by the independent variable (x), or r^2. ranges from 0 to 1

dependent variable

the variable to be predicted, designated as y

if the correlation coefficient between two variables is +1

there is a perfect positive relationship between the two sets of numbers