Stat 252 Regression & Correlation
the difference between the total variation & the unexplained variation a. is the standard error of the estimate b. is the coefficient of determination c. is equal to the explained variation d. equals 1 when r=1
c. is equal to the explained variation
if, in the population regression equations, B is positive, we say that there is linear relationship between X & Y a. an inverse b. a significant c. a direct d. no
c. a direct
the quantity ????? is called the sum of squares a. least b. total c. explained d. unexplained
c. explained
the variable that can be manipulated by the investigator is called the a. dependent variable b. unit of association c. independent variable d. discrete variable
c. independent variable
the prediction interval for an individual response will be narrower than the confidence interval for ???
false
the range of the coefficient of determination is -1 to +1
false
the slope of the line regression represents the unit change in X per unit change in Y
false
the standard deviation of the observed Y values around the average Y is called the standard error of the estimate
false
the value of r is always positive
false
regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two quantitative variables
true
regression analysis is used for the purpose of prediction
true
the Y intercept (b0) represents the predicted value of Y when X=0
true
the closer the standard error of the estimate is to zero, the better the model fits the observed data
true
if all the points in a scatter diagram lie on the line of regression, the value of the standard error of the estimate is zero
true
the Principle of Least Squares states that the sum of the squared deviations between the actual Y values & predicted by the regression line is a. a minimum b. a maximum c. 0 d. 1
a. a minimum
in multiple regression analysis the independent variables are sometimes referred to as variables a. partial b. transformation c. dependent d. explanatory
d. explanatory
the relationship among several variables may be described geometrically by some a. a regression surface b. sphere c. hypersphere d. straight line
a. a regression surface
the graph of X, Y pairs represented by dots is called a. a scatter diagram b. a frequency histogram c. an influence plot d. a normal probability plot
a. a scatter diagram
if, as X increases, Y tends to decrease, we say there is linear relationship between X & Y a. an inverse b. a significant c. a direct d. no
a. an inverse
if, in the population regression equations, B is negative, we say that there is linear relationship between X & Y a. an inverse b. a significant c. a direct d. no
a. an inverse
in the regression & correlation analysis, the measure whose values are restricted to the range 0 to 1, inclusive, is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation of coefficient
a. coefficient of determination
the variable about which the investigator wishes to make predictions or estimation is called the a. dependent variable b. unit of association c. independent variable d. discrete variable
a. dependent variable
any prediction based on this picture would a. have no error b. be of little or no use c. none of these are correct
a. have no error
the quantity ????? is called the sum of squares a. least b. total c. explained d. unexplained
a. least
the Y intercept (b0) represents the a. predicted value of Y when X=0 b. change in Y per unit change in X c. predicted value of Y d. variation around the line of regression
a. predicted value of Y when X=0
in this particular problem, the researcher is trying to predict a. quantity demanded based on price b. price based on quantity demanded c. both price & quantity demanded d. none of these are correct
a. quantity demanded based on price
testing for the existence of correlation is equivalent to a. testing for the existence of the slope (b1) b. testing for the existence of the Y intercept (b0) c. the confidence interval estimate for predicting Y d. none of the above
a. testing for the existence of the slope (b1)
if all the points in a scatter diagram lie on the line of regression, the value of the standard error of the estimate is a. zero b. one c. equal to the slope d. none of the above
a. zero
in a simple linear regression, the sign of the coefficient of correlation is a. always positive with business data b. always the same as the sign of the slope c. determined by the degree of scatter d. determined by the sign of the coefficient of determination
b. always the same as the sign of the slope
the strength of the linear relationship between two variables may be measured by the a. scatter diagram b. coefficient of correlation c. slope d. Y intercept
b. coefficient of correlation
r2 is the a. coefficient of correlation b. coefficient of determination c. slope d. standard error of the estimate
b. coefficient of determination
the variable used to predict another variable is called the a. dependent variable b. independent variable c. correlation variable d. students t variable e. none of these are correct
b. independent variable
in simple linear regression, when the coefficient of correlation between two variables is zero, the regression line a. goes through the origin b. is horizontal c. is vertical d. has a negative slope
b. is horizontal
in a simple linear regression problem, r & b1 a. may have opposite signs b. must have the same sign c. must have opposite signs d. are equal
b. must have the same sign
in regression analysis, the quantity that gives the amount by which Y changes for a unit change in X is called the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation of coefficient
b. slope of the regression line
in the equation y=a+bx, b is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation of coefficient
b. slope of the regression line
the interpretation of the standard error of the estimate is analogous to that of the a. mean b. standard deviation c. slope d. Y intercept
b. standard deviation
the slope (b1) represents a. predicted value of Y when X=0 b. the change in Y per unit change in X c. the predicted value of Y d. variation around the line or regression
b. the change in Y per unit change in X
assuming a linear relationship between X & Y, if the coefficient of correlation (r) equal -.30, a. there is not correlation b. the slope (b1) is negative c. variable X is larger than variable Y d. the variance of X is negative
b. the slope (b1) is negative
in performing a regression analysis involving two quantitative variables, we are assuming a. the variances of X & Y are equal b. the variation around the line of regression is the same for each X value c. that X & Y are independent d. all of the above
b. the variation around the line of regression is the same for each X value
the standard error of the estimate is a measure of a. total variation b. the variation around the regression line c. explained variation d. the variation of the X variable
b. the variation around the regression line
in regression & correlation analysis, the entity on which sets of measurements are taken is called a. dependent variable b. unit of association c. independent variable d. discrete variable
b. unit of association
in the regression equation for the straight line, the value of b would be about a. -1.00 b. +1.00 c. 0 d. none of these are correct
c. 0
if, as X increases, Y tends to increase, we say there is linear relationship between X & Y a. an inverse b. a significant c. a direct d. no
c. a direct
the method used to arrive at the "best-fitting" straight line in regression analysis is referred to as the a. freehand method b. non determination method c. least squares method d. correlation method e. none of these are correct
c. least squares method
if computed, the sign of b in the equation would be a. either positive or negative b. postive c. negative d. infinity e. none of these are correct
c. negative
the independent variables in regression analysis are sometimes referred to as variables a. response b. multiple c. predictor d. simple
c. predictor
the picture is called a a. dotted swiss chart b. bar chart c. scatter diagram d. straight-line chart e. none of these are correct
c. scatter diagram
if the correlation coefficient (r)=1.00, then a. the Y intercept (b0) must equal zero b. the explained variation equals the unexplained variation c. there is no unexplained variation d. there is no explained variation
c. there is no unexplained variation
in the equation y=a+bx, a is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation of coefficient
c. y intercept of the regression line
the standard error of estimate, if computed, would be a. infinity b. +1.00 c. -1.00 d. 0 e. none of these are correct
d. 0
the width of the confidence interval estimate for the predicted value of Y is dependent on a. the standard error of the estimate b. the value of X for which the prediction is being made c. the sample size d. all of the above
d. all of the above
the value of r^2 for a particular situation is .49. What is the coefficient of correlation in this situation? a. .49 b. .70 c. .07 d. cannot be determined from the information given
d. cannot be determined from the information given
in simple linear regression, when the coefficient of correlation between two variables is zero, the regression line goes through the origin
false
in the regression & correlation analysis, the measure whose values are restricted to the range -1 to +1, inclusive, is the a. coefficient of determination b. slope of the regression line c. y intercept of the regression line d. correlation of coefficient
d. correlation of coefficient
if, as X increases, Y is just as likely to decrease as increase, we say that there is linear relationship between X & Y a. an inverse b. a significant c. a direct d. no
d. no
if, in the population regression equations, B=0, we say that there is linear relationship between X & Y a. an inverse b. a significant c. a direct d. no
d. no
if the dependent variable increases as the independent variable increases in a regression equation, then the coefficient of correlation would be in the range a. 0 to -1 b. 0 to -.5 c. 0 to -2 d. none of the above
d. none of the above
the graph of the observation obtained as part of a regression or correlation analysis is called a a. frequency polygon b. frequency distribution c. histogram d. scatter diagram
d. scatter diagram
the coefficient of determination (r^2) tells us a. that the coefficient of correlation (r) is larger than one b. whether r has any significance c. that we should not partition the total variation d. the proportion of total variation that is explained
d. the proportion of total variation that is explained
the quantity ????? is called the sum of squares a. least b. total c. explained d. unexplained
d. unexplained
the equation for the line going through the points wold take the form of a. Y= a + b + c b. Y= a + bX or Y= a - bX c. Y = X - 1 d. Y = a +bX^2 e. none of these are correct
e. none of these are correct
correlation measures the degree of association between two variables
false
in scatter diagrams, the independent variable goes on the vertical axis & the dependent variable goes on the horizontal axis
false
when r=-1, it indicates a perfect relationship between X & Y
true
