Stat Conceptual

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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


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