Noteset 3: Linear Regression

If r=.632, what is r squared? What does this value indicate?

39.9%, it means that 39.9% of the variation in y can be attributed to x

In the linear regression model, y-hat represents the a. expected or predicted value of y b. the slope c. the y-intercept d. the slope

a. expected or predicted value of y

When using linear regression to analyze data, we call the x variable the a. explanatory or independent variable b. response or dependent variable c. the residual d. the slope

a. explanatory or independent variable

Four areas to consider when viewing bivariate data are a. the pattern, the direction, variation between observed and expected values, outliers b. mean, median, mode, standard deviation c. experiment, boxplot, mean, mode d. boxplot, median, scatterplot, experiment

a. the pattern, the direction, variation between observed and expected values, outliers

Interpolation occurs when predictions are made a. within the observed data values b. outside the observed data values

a. within the observed data values

A value of .458 represents a. no linear relationship between x and y b. a weak relationship between the variables x and y c. a strong relationship between the variables x and y d. r cannot be positive

b. a weak linear relationship between the variables x and y

We use linear regression to analyze a. univariate data b. bivariate data c. trivariate data d. multivariate data

b. bivariate data

Extrapolation occurs when a. predictions are made within the observed values b. predictions are made outside the observed values

b. predictions are made outside of the observed values

The linear regression model is generally a a. deterministic model b. probabilistic model c. curvilinear model d. constant model

b. probabilistic model

The closer the observed values are to the regression line, the a. weaker the relationship is between the two variables b. stronger the relationship is between the two variables

b. stronger the relationship is between the two variables

A scatterplot is a method of displaying a. univariate data b. the observed bivariate values gathered from an experiment or observation c. scatterplots do not represent anything d. a histogram

b. the observed bivariate values gathered from an experiment or observation

When using linear regression to analyze data, we call the y variable the a. explanatory variable or independent variable b. the response or dependent variable c. the residual d. the y-intercept

b. the response variable or the dependent variable

A r value of -.95 represents a. no linear relationship between the variables x and y b. a weak relationship between the variables x and y c. a strong relationship between the variables x and y d. r cannot be negative

c. a strong relationship between the variables x and y

If we square the correlation coefficient r we get the a. slope of the regression equation b. y-intercept of the regression equation c. coefficient of determination d. nothing because you cannot square r

c. coefficient of determination

In the linear regression model, the slope (b1) can be interpreted as the a. expected or predicted value of y b. the value of y when x=0 c. the average increase in y-hat for a one unit increase in x d. there is no slope in the linear regression equation

c. the average increase in y-hat for a one unit increase in x

The coefficient of determination represents a. the direction of the relationship b. the beginning of the relationship c. the portion of variation in y that can be attributed to x

c. the portion of variation in y that can be attributed to x

The residuals represent the a. strength of the relationship between two variables b. the direction of the relationship between the two variables c. the prediction error for any observed y values d. the correlation coefficient

c. the prediction error for any observed y values

Residuals are calculated by a. the regression equation b. the correlation coefficient c. the coefficient of determination d. the formula (observed - expected) or y - y-hat)

d. the formula (observed - expected) or (y - y-hat)

The x in the linear regression model represents the a. expected or predicted value of y b. the y-intercept c. the slope d. the independent or explanatory variable

d. the independent or explanatory variable

r will a. always take on values between -1 and 1 inclusive b. be stronger the closer it is to -1 or 1 c. indicate a perfect relationship if it is equal to 1 or -1 d. indicate no relationship if it is equal to 0 e. all of the above

e. all of the above