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