Stat 252- Linear Regression Multiple choice Exam

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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


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