Definitions

Sb measures

how consistent the slope of a regression equation would be if several sets of samples from the population were selected and the regression equation were derived for each of them.

Hypothesis test for population slope determines

if slope (B1) is equal to zero

A correlation coefficient indicates

The strength and direction of the linear relationship between an independent and dependent variable

Homoscedasticity

The variation of a dependent variable is the same across all values of an independent variable

Independent variable

a variable that explains the variation in the dependent variable

Dependent variable

a variable that is explained by the independent variable

a regression equation provides

a point estimate for a dependent variable, given the value of an independent variable

The least squares method is a method of finding the linear equation that best fits

a set of ordered pairs

the coefficient of determination is the ____ of the correlation coefficient

square

Se measures

the amount of dispersion of the observed data around the regression line

SSR measures

the amount of variation in a dependent variable explained by an independent variable

population correlation coefficient refers to

the correlation between all values of two variables of interest in a population

residual is

the difference between the actual data value and the predicted value

regression line

the line created by a regression analysis that best fits the data

failing to reject the null hypothesis for population slope means

there is no linear relationship between the dependent and independent variables

r=0 means

there is no linear relationship between the x and y variables

SSE measures

variation in a dependent variable that is explained by variables other than the independent variable

Normal Probability Plot is used for _____ and is done by _____

verifying if the data follow the normal probability distribution by graphing the data on the y-axis and the z-scores for the data on the x-axis

Rejecting the null hypothesis for population correlation coefficient means

we have enough evidence to conclude that a linear relationship does exist between the two variables

The direction in which the relationship between independent and dependent variables exists

x to y

variable for y intercept

B0

hypothesis test for population correlation coefficient determines ____ and is based on ____

if the population correlation coefficient (p) is significantly different from 0 based on the sample correlation coefficient, (r)

R^2=0 means

there is no linear relationship between the variables

Range of values of r

-1.0 to +1.0

variable for population slope

B1

If the confidence interval for a regression slope includes 0

B1 could be equal to 0, there may not be a linear relationship between independent and dependent variables

Independent variable (x)

Explains the variation in a dependent variable (y)

Variable for the sample coefficient of determination

R^2

Variable for standard error of slope

Sb

variable for the standard error of the estimate

Se

SSE stands for

Sum of Squares Error

SSR stands for

Sum of Squares Regression

SST is

The difference in the values of the dependent variables

SST stands for

Total sum of squares

In the LSM, the value of y represents

an actual data point

Constructing a confidence interval for the regression slope provides

an estimate for the possible values of B1

Confidence intervals are for

average values of y

The least squares method involves finding values for

b0 (the y-intercept), and b1 (the slope)

residual variable

ei

The residuals must

exhibit no patterns

Prediction intervals are for

individual values of y

The relationship between the independent and dependent variables must be

linear

The residuals must follow

normal probability distribution

Population correlation coefficient variable

p

variable for population correlation coefficient

p

Population coefficient of determination variable

p^2

Variable for sample correlation coefficient

r

The coefficient of determination measures

the percentage of the total variation of a dependent variable explained by an independent variable

Population coefficient of determination measures

the percentage of total variation of the dependent variable that is explained by the independent variable

In the LSM, the value of y hat represents

the predicted value of y using the linear equation

The variation of the dependent variable must be

the same across all values of the independent variable