Stat Conceptual
in a simple regression analysis (where Y is a dependent and X an independent variable), if the Y-intercept is positive, then
answer on packet was "none of the above answers are correct"
if, as x increases, y is just as likely to decrease as increase, we say that there is _________ linear relationship between x and y
no
if, in the population regression equations, beta = 0, we say that there is ___________ linear relationship between x and y
no
the equation for the line going through the points would take the form of
none of these are correct
in a simple linear regression, the sign of the coefficient of correlation is
always the same sign of the slope
if computed, the sign of b in the equation would be
negative (because declining slope)
if the dependent variable increases as the independent variable increases in a regression equation, then the coefficient of correlation would be in the range
(answer was none of the above)
*scatter diagram showing a horizontal line with dot all around it* in the regression equation for the straight line, the value of b would be about
0
If all the points of a scatter diagram lie on the line of regression, the value of the standard error of the estimate is
0
the standard error of estimate, if computed, would be
0
If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is
1
Regression analysis is a statistical procedure for developing a mathematical equation that describes how
1 dependent and 1 or more independent variables are related
if the coeifficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the variation in the independent variable is
16%
if the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is
64%
if the coefiificent of determination is 0.9, the percentage of variation in the dependent variaible explained by the variation in the independent variable is
90%
the principle of least squares states that the sum of the squared deviations between the actual y values and the values predicted by the regression line is
a minimum
the relationship among several variables may be described geometrically by some
a regression surface
the graph of x, y pairs represented by dots is called
a scatter diagram
If the coefficient of determination is equal to 1, then the coefficient of correlation
can be either -1 or +1
the value of r^2 for a particular situation is .49. What is the coefficient of correlation in this situation?
cannot be determined because we should know if it's - or +
the slope (b1) represents the
change in y per unit change in x
the strength of the linear relationship between two variables may be measured by the
coefficient of correlation
in the regression and correlation analysis, the measure whose value are restricted to the range 0 to 1, inclusive, is the
coefficient of determination
r^2 is the
coefficient of determination
the coefficient of correlation is the square root of the
coefficient of determination
in the regression and correlation analysis, the meausre who value are restricted to the range -1 to +1, inclusive, is the
correlation coefficient
If the coefficient of determination is a positive value, then the regression equation
could have either a positive or negative slope
in a regression analysis, the variable that is being predicted is the
dependent variable
in regression analysis, the independent variable is used to predict the
dependent variable
in regression analysis, the response variable is the
dependent variable
in regression analysis, the variable that is being predicted is the
dependent variable
the variable about which the invesitgator wishes to make predictions or estimation is called the
dependent variable
if, as x increases, y tends to increase, we say there is _______ linear relationship between x and y
direct
if, in the population regression equations, beta is positive, we say that there is ___________ linear relationship between x and y
direct
if there is a very strong correlation between two variables, then the coefficient of correlation must be
either +/- 1
the quantity E(y hat - ybar)^2 is called the
explained sum of squares
the difference between the total variation and the unexplained variation is equal to the
explained variation
in multiple regression anaylsis, the independent variables are sometimes referred to as
explanatory variables
T OR F: in a simple linear regression, when the coefficient of correlation between two variables is zero, the regression line goes through the origin
false
T OR F: in scatter diagrams, the independent variable goes on the vertical axis and the dependent variable goes on the horizontal axis
false
T OR F: the prediction interval for the individual response will be narrower than the confidence interval for uyx
false
T OR F: the slope of the line regression represented the unit change in x per unit change in y
false
T OR F: the standard deviation of the observed y values around the average y is called the standard error of estimate
false
T OR F: the value of r is always positive
false, can be -/+
T OR F: the range of the coefficient of determination is -1 to +1
false, it's 0 to 1
any predictions based on this picture would
have no error
in simple linear regression, when the coefficient of correlation between the two variables is zero, the regression line is
horizontal
a multiple regression model has more than one
independent variable
the variable that can be manipulated by the investigator is called the
independent variable
the variable used to predict another variable is called the
independent variable
in multiple regression analysis, there can be several
independent variable, but only one dependent variable
if, as x increases, y tends to decrease, we say there _________ linear relationship between x and y
inverse
if, in the population regression equations, beta is negative, we say that there is ___________ linear relationship between x and y
inverse
if the coefficient of determination is 0.81, the coefficient of correlation
is -/+ .9 (none of the above answers)
Larger values of r2 imply that the observations are more closely grouped about the
least squares line
a procedure used for finding the equation of a straight line which provides the best approximation for the relationship between the independent and dependent variables is the
least squares method
the method used to arrive at the best-fitting straight line in regression analysis is referred to as the
least squares method
If the coefficient of correlation is a negative value, then the coefficient of determination
must be positive
in a simple linear regression problem, r and b1
must have the same sign
if the coefficient of the correlation is a positive value, then the slope of regression line must also be
positive
the y-intercept (bo) represents the
predicted value of y when x = 0
the independent variables in regression analysis are sometimes referred to as
predictor variables
in this particular problem, the researcher is trying to predict
quantity demanded based on price
the equation that describes how the dependent variable (y) is related to the independent variable (x) is called the
regression model
*graph with a declining line with dots on the line* this graph is called a
scatter diagram
the graph of the observations obtained as part of a regression or correlation analysis is called a
scatter diagram
in a regression analysis, the quatitiy that gives the amount by which y changes for a unit change is called the
slope of the regression line
in the equation Y^ = a + bx, b is the
slope of the regression line
the interpretation of the standard error of the estimate is analogous to that of the
standard deviation
the width of the confidence interval estimate for the predicted value of y is dependent on
standard error of the estimate, value of x for which the prediction is being made, and sample size (all of the above)
Testing for the existence of correlation is equivalent to
testing for the existence of the slope (b1)
the coefficient of determination (r^2) tell us
the proportion of total variation that is explained
Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals -0.30:
the slope (b1) is negative
Correlation analysis is used to determine
the strength of the relationship between the dependent and the independent variables
the standard error of the estimate is a measure of
the variation around the regression line
the quantity E(yi - y bar)^2 is called the
total sum of squares
T OR F: correlation measures the degress of association between two variables
true
T OR F: if all the points in a scatter diagram lie on the line regression, the value of the standard error of the estimate is zero
true
T OR F: regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two quantitative variables
true
T OR F: regression analysis is used for the purpose of prediction
true
T OR F: the closer the standard error of the estimate is to zero, the better the model fits then observed data
true
T OR F: the y-intercept (bo) represents the predicted value of y when x = 0
true
T OR F: when r = -1, it indicates a perfect relationship between x and y
true
the quantity E(yi - y hat)^2 is called the
unexplained sum of squares
if the correlation coefficient (r) = 1.00, then there is no
unexplained variation
in regression and correlation analysis, the entitiy on which sets of measurements are taken is called the
unit of association
in performing the regression analysis involving two quantitative variables, we are assuming the
variation around the line of regression is the same for each x value
in the equation Y^ = a + bx, a is the
y-intercept of the regression line
