Reading 4

Frage	Antworten
What is multiple regression?	An extension of simple regression to the situation where there are 2 or more independent variables.
What is the general formula of a multiple regression line?	Y’ = a + b1X1 + b2X2 + ….. + bkXk
What indicates the unique effect of an independent variable, above and beyond the effect of other independent variables in the analysis?	Slope
A schematic diagram in which the variance of a variable is represented by the area of a circle, and the relationships among variables are represented by areas of overlap among circles.	Ballantine Diagram
In multiple regression, what needs to be done to calculate the slope of X1?	The effect of X2 needs to be removed.
What 2 equations are adjusted in multiple regression?	Slope (b) and Standard error (SEb).
As the relationship between Xs increases, does the standard error increase, stay the same, or decrease?	Increase
In multiple regression, what is the goodness of fit ratio called?	Squared multiple regression (R^2)
True/False: In general, the squared multiple correlation is equal to the sum of the two squared simple correlations. (R^2 = rY1^2 + rY2^2).	False (area b, the area shared between both squared simple correlations, is counted twice)
Which should be a larger value: squared multiple correlation (R^2) or adjusted squared multiple correlation (Radj^2)?	Squared multiple correlation (R^2)
How would you obtain a value of R^2 closer to the average R^2?	Repeat the analysis innumerable times using a series of similar samples.
Which provides a more realistic estimate of the goodness of fit: Squared multiple correlation or Adjusted squared multiple correlation?	Adjusted squared multiple correlation
Why is an Adjusted squared multiple correlation sometimes called a shrunken R^2?	It is always smaller than the sample R^2.
What is the degrees of freedom of standard error equal to?	Sample size (N) - # of X variables (k) - 1
What is the situation called when the squared simple correlation is equal to 1.0?	Exact collinearity
What cannot be calculated if the squared simple correlation is equal to 1.0?	Standard error
What is the situation called when the simple squared correlation is near 1.0?	Multicollinearity
As the squared correlation between the independent variables increases, does the standard error of the slope increase, stay the same, or decrease?	Increase
As the standard error increases, does the confidence interval increase, stay the same, or decrease?	Increase
What condition makes it difficult to separate the effects of individual independent variables?	The independent variables become more and more correlated.
True/False: There is always some uncertainty about the true slope of each independent variable.	True
What are the 2 ways to address the uncertainty around the slope?	1. Calculate the t ratio for each slope 2. Calculate the confidence intervals for each slope
What is the way to address the uncertainty of the squared multiple correlation (R^2)?	Calculate the F ratio
What represents the overall effect of the independent variables?	Goodness of fit ratio (R^2)
If SE1 has a SS1 4x greater than SS2, what is the value of SE2 relative to SE1?	SE2 = 2 x SE1
If you have a 90% confidence interval, what is the percentage for alpha?	10%
As the value of Fcalc decreases, does the value of tcalc increase, stay the same, or decrease?	Decrease
When do you use the adjusted squared multiple correlation (Radj^2) instead of the squared multiple correlation (R^2)?	Radj^2 is much smaller than R^2.
What is df1 and df2 for Fcalc?	df1 = k df2 = N - k - 1
Which do you use if there is no clear evidence of a variable's effect: Simple regression line or Multiple regression line?	Simple regression line (Since only 1 variable has a statistically significant effect on the dependent variable)
What does a curvilinear regression line allow the goodness of fit to do?	It allows the goodness of fit to fit the sample better in some cases.
What is the equation for a curvilinear regression line?	Y' = a + b1X + b2X^2
Y' = a + b1X + b2X^2 Which term in this equation allows the curved line of best fit?	b2X^2
How many independent variables are in the curvilinear regression line?	1 independent variable
As SP12 and r12 increase, does tcalc increase, stay the same, or decrease?	Decrease
The likelihood of a correct positive.	Power
True/False: Standardization of slope gives a mean of 0 and a standard deviation of 1.	True
A standardized slope expresses the effect of an independent variable in terms of what?	In terms of z scores.
Why is the constant omitted from the equation for the standardized regression line?	The constant is always 0 for a standardized regression line.
What is the value for standardized sums of squares?	SS = N - 1
What are the values of the means for each of the variables for a standardized regression line?	Always 0 since it is a mean of z scores.
How do you standardize the slope?	Bk = bk x sk/sY Bk = bk x sqrt(SSk/SSY)
True/False: The equations for a non-standardized regression line can be used with the standardized SS and SP.	True
True/False: The standardized tcalc is equal to the non-standardized tcalc.	True
True/False: The issue of statistical significance depends on the units.	False
How do you find the constant in multiple regression with categorical variables?	a = M0
How do you find the slope of X2 in multiple regression with categorical variables?	b2 = M2 - M0
How many columns of dummy coding do you need for 4 categorical variables?	3 (Always 1 less than the number of X variables)

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