Stat 252- Linear Regression Multiple choice Exam
In the equation Y^hat = a+ bx, a is the
"Y intercept" of the regression line
In the equation Y^hat = a +bx, b is the
"slope" of regression line
The width of the confidence interval estimate for the predicted value of Y is dependent on
-the standard error of estimates -the value of X for which the prediction is being made -the sample size
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... The coefficient of determination will be equal to 1 since all the data points on scatter diagram lie directly along the least square regression.
If the coefficient of correlation (r) is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is
64%. Given coefficient of correlation r = 0.8, then r2 = 0.8*0.8 = 0.64
If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable
90% because ...
If the coefficient of correlation (r) is a positive value, then the slope of the regression line must
Also be positive. If coefficient of correlation is positive, it means that when X increases, Y also increases, so slope will be positive.
In a simple linear regression, the sign of the coefficient of correlation (r) is
Always the same as the sign of the slope
If, in the population regression equations, β is positive, we say that there is ____________ linear relationship between X and Y.
An inverse
In regression analysis, the response variable is the
Dependent Variable
In regression analysis, the variable that is being predicted is the
Dependent Variable
In regression analysis, the variable that is being predicted is the
Dependent variable
The variable about which the investigator wishes to make predictions or estimations is called the
Dependent variable
The difference between the total variation and the unexplained variation is
Equal to the explained variation
The quantity Σ("Y^hat"- "mean of Y")^2 is called the ______________ sum of squares.
Explained
In multiple regression analysis the independent variables are sometimes referred to as ___________ variables.
Explanatory variables
The prediction interval for an individual response will be narrower than the confidence interval for Uyx (Mu sub yx).
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 coefficient of correlation (r) is always positive.
False. It can be between -1 and +1. So therefore it can be negative as well.
In simple linear regression, when the coefficient of correlation between two variables is zero, the line of regression line goes through the origin
False. It is horizontal
In scatter diagrams, the independent variable goes on the vertical axis and the dependent variable goes on the horizontal axis.
False. The independent variable goes on the horizontal axis and the dependent variable goes on the vertical axis.
The range of the coefficient of determination (r^2) is -1 to +1
False. The range for coefficient of correlations (r) is between -1 and +1. While (r2) is between 0 to 1.
The slope of the line regression represents the unit change in X per unit change in Y
False. The slope of the line regression (b) represents the rate of change in y as x changes
In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then
In a simple regression analysis, Y intercept does not specify any information about the relation between X and Y. It is specified by the slope of the regression line. So E. none of the answers are correct.
The variable used to predict another variable is called the
Independent Variable
The variable that can be manipulated by the investigator is called the
Independent variable
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, as X increases, Y is just as likely to decrease as increase, we say that there is _________ linear relationship between X and Y.
No linear relationship
If, in the population regression equations, β = 0, we say that there is ____________ linear relationship between X and Y.
No linear relationship
Regression analysis is a statistical procedure for developing a mathematical equation that describes how
One dependent and one or more independent variables are related
If the coefficient of correlation (r) is a negative value, then the coefficient of determination (r2) must be
Positive. Because a negative value multiplied by a negative value equals a positive value. -r* -r = + COD
In regression analysis, the independent variable is used to
Predict the dependent variable
The Y intercept (b sub 0) represents the
Predicted value of Y when X = 0
The independent variables in regression analysis are sometimes referred to as ____________ variables.
Predictor
The relationship among several variables may be described geometrically by some ____________.
Regression Surface
The coefficient of correlation (r) is the
Square root of the coefficient of determination (r2)
The quantity Σ(Yi - "mean of Y")^2 is called the ______________ sum of squares.
Total
Correlation measures the degree of association between two variables
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 0
True
Regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two quantitive variables.
True
Regression analysis is used for the purpose of the prediction
True
The Y intercept (b0) represents the predicted value of Y when X = 0
True
The closer the standard area of the estimate is to zero, the better the model fits the observed data
True
When r = -1, it indicates a perfect relationship between X and Y
True
The quantity Σ(Yi - "Y^hat")^2 is called the ______________ sum of squares.
Unexplained
In regression and correlation analysis, the entity on which sets of measurements are taken is called the
Unit of Association
If the dependent variable increases as the independent variable increases in a regression equation, then the coefficient of correlation (r) would be in the range
When both variables increase the result is positive. r= +1
Scatter diagram
a graph that shows the degree and direction of relationship between two variables
coefficient of correlation (r)
a measure of correlation that ranges in value from -1.00 to +1.00
The Principle of Least Squares states that the sum of the squared deviations between the actual Y values and the predicted by the regression line is
a minimum
The graph of X, Y pairs represented by dots is called
a scatter diagram
line of regression
also known as the "line of best fit"; a line that best passes through or near graphed data; used to describe data and predict where new data will appear on the graph
If, as X increases, Y tends ti decrease, we say there is ________ linear relationship between X and Y.
an inverse
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
r^2 is the
coefficient of determination
In the regression and correlation analysis, the measure whose values are restricted to the range 0 to 1, inclusive, is the
coefficient of determination (r2)
If the coefficient of determination (r2) is equal to 1, then the coefficient of correlation (r) can be
either -1 OR +1 (not in-between)
If the coefficient of determination (r2) is a positive value, then the regression equation could have
either a positive or negative slope
In simple linear regression, when the coefficient of correlation between two variables is zero, the line of regression line
is horizontal
A multiple regression model has
more than one independent variable
If there is a very strong correlation between two variables, then the coefficient of correlation (r) must
must either be close to -1 or 1. So none of the above answers are correct
In a simple linear regression problem, r and b1
must have the same sign
The coefficient of determination (r^2) tell us the
proportion of total variation that is explained
The graph of the observations obtained as part of a regression or correlation analysis is called a
scatter diagram
In multiple regression analysis, there can be
several independent variables, but ONLY ONE dependent variable
In regression analysis, the quantity that gives the amount by which Y changes for a unit change in X is called the
slope of regression line
If the coefficient of determination (r2) is 0.81, the coefficient of correlation (r)
solve by: using square root of coefficient of determination
The interpretation of the standard error of the estimate is analogous to that of the
standard deviation
Testing for the existence of correlation is equivalent to
testing for the existence of the slope (b sub 1)
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
the regression model
Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals -0.30:
the slope (b sub 1) is negative
The coefficient of correlation is
the square root of the coefficient of determination
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
In performing a regression analysis involving two quantitive variables, we are assuming the
variation around the line of regression is the same for each X value
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
