QBA Final Regression Analysis
The correlation coefficient between two variables, X and Y, would equal ____ if the coordinate points of the scatter chart fell exactly on a downward sloping straight line.
-1
If all the points fall on a straight line, the value of r will be _____ or ____.
-1 or 1
A correlation coefficient between 2 variables, X and Y, can range between _____ and _______.
-1 to 1
The range of r is from _______ to ________.
-1 to 1
If two quantitative variables are not straight line related, you would expect the correlation coefficient to be approximately _____________.
0
R^2, the coefficient of determination, for 2 variables, X and Y, can range between _______ and _______.
0 to 1
The coefficient of determination was computed to be 0.38 in a problem involving one independent variable and one dependent variable. This result means
38 percent of the total variation in the dependent variable is accounted for by the independent variable
If correlation coefficient between two variables, X and Y, equals +.80, then _____% of the variation in the Y variable can be "explained" by the simple linear relationship with the X variable.
64
When the correlation coefficient is significant, one can assume X causes Y.
False. It only suggests that there is a strong linear association between the two variables. Correlation never establishes a cause/effect relationship, just a trend.
It is not possible to have a significant correlation by chance alone.
False. Two variables may be linearly associated by just pure coincidence
A negative relationship between two variables means that for the most part, as the X variable increases, the Y variable increases.
False. What is described corresponds to a positive relationship. Negative meanse inverse, so as X increases, Y decreases.
The X variable is called the ________ variable.
Independent
One should expect the correlation coefficient relating the weight of a person to the person's height to be ___________
Positive
What is the relationship between the coefficient of determination and the coefficient of correlation?
The coefficient of determination is the coefficient of correlation squared
A coefficient of correlation was computed to be -0.98. This result means:
The relationship between two variables is very strong and negative
If all the points are on the regression line, then
The standard error of the estimate is 0.
A correlation coefficient of -1 implies a perfect linear relationship between the variables
True
Even if the correlation coefficient is high or low, it may not be significant.
True
In simple linear regression, there is one dependent variable and one independent variable.
True
The independent variable is typically plotted on the ____ axis on an "XY" scatter chart.
X
The slope of the straight-line, Y=m*X + b, measures the change in _____ given a unit increase in ________.
Y,X
The ________________ of a correlation coefficient measures the direction of the relationship between two quantitative variables.
algebraic sign
The coefficient of determination for two variables, X and Y, can be calculated by simply multiplying the ________________ for X and Y by itself.
correlation coefficient (r)
In a regression analysis, the variable that is being predicted is called the _____ variable.
dependent
A high correlation between two variables, X and Y, ______ proves that changes in X cause changes in Y.
does not
The regression line is called the _________.
least squares line or line of best fit
The strength of the linear relationship between two variables is determined by the value of
r
The coefficient of determination is
r^2
The algebraic sign of the correlation coefficient and the slope of the regression line will always be the _______
same
A statistical graph of two variables is called a
scatterplot
The sign of r and of _______ will always be the same.
the slope
An "outlier" or atypical value in a set of numbers is usually defined by any number that is ______ standard deviation above or below the mean of the numbers.
three
A correlation coefficient __________ be the appropriate data summary to see if a student's gender was related to their major in college.
would not; because the variables are qualitative
The equation of the regression line used in statistics is
y = b0 + b1*x
An error (or residual) is defined as:
y-y^
