Deck 17: Regression

Question 1

What criterion do we use to decide on the "least squares regression" line through data?

A) It is the line for which the sum of all the deviations between the points and the line (in the X direction) is minimized.
B) It is the line for which the sum of all the deviations between the points and the line (in the Y direction) is minimized.
C) It is the line for which the sum of all the squared deviations between the points and the line (in the X direction) is minimized.
D) It is the line for which the sum of all the squared deviations between the points and the line (in the Y direction) is minimized.

Answer 1

D

Question 2

Which of the following equations describes a line that passes through the point (15,51)?

A) Y = 2 + 5X
B) Y = 4 + 4X
C) Y = 6 + 3X
D) Y = 7 + 2X

Answer 2

C

Question 3

Which of the following equations describes a line that passes through the point (4,12)?

A) Y = 20 - 2X
B) Y = 25 - 3X
C) Y = 30 - 4X
D) Y = 35 - 5X

Answer 3

A

Question 4

Which of the following equation defines the line with the largest slope and Y-intercept?

A) Y = 12 + 9X
B) Y = 12 + 6X
C) Y = 15 + 9X
D) Y = 15 + 6X

Question 5

If the linear least squares equation for a data set is Y = 12 - (0.7)X, what is the residual corresponding to a data point with a value of (8, 8)?

A) -1.6
B) 0
C) 1.6
D) 3.5

Question 6

If the linear least squares equation for a data set is Y = 2 + (0.4)X, what is the residual corresponding to a data point with a value of (9, 4)?

A) -0.4
B) 0.4
C) 0.8
D) -1.6

Question 7

If the slope is -1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the standard error of the slope?

A) 0.215
B) 0.310
C) 0.833
D) 1.200

Question 8

If the slope is -1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the 95% confidence interval of the slope?

A) -4.214 to 0.934
B) -3.562 to 0.282
C) -2.840 to -0.440
D) -2.133 to -1.115

Question 9

Which of the following is true for 95% confidence bands?

A) 95% of the population data will be bracketed by the 95% confidence bands.
B) 95% of the sample data will be bracketed by the 95% confidence bands.
C) The 95% confidence bands from 95% of samples will bracket the true population regression line.
D) There is a 95% chance that the sample regression will match the true population regression line.

Question 10

Consider the partially completed ANOVA table showing the results of a regression analysis shown.
?
$\begin{array}{|lcrcl|}\hline \text { Source of } & {\text { Sum of }} & {\text { Mean }} & \\\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\\text { Regression } & 305.1 & 1 & ? & ? \\\text { Residual } & 1247.3 & 24 & ? & \\\text { Total } & 1552.4 & 25 & & \\\hline\end{array}$

-What is the F-ratio?
?

A) 1.245
B) 4.088
C) 5.088
D) 5.871

Question 11

Consider the partially completed ANOVA table showing the results of a regression analysis shown.
?
$\begin{array}{|lcrcl|}\hline \text { Source of } & {\text { Sum of }} & {\text { Mean }} & \\\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\\text { Regression } & 305.1 & 1 & ? & ? \\\text { Residual } & 1247.3 & 24 & ? & \\\text { Total } & 1552.4 & 25 & & \\\hline\end{array}$

-What is the R² value?
?

A) 0.197
B) 0.245
C) 0.755
D) 0.803

Question 12

Consider the partially completed ANOVA table showing the results of a regression analysis shown.
?
$\begin{array}{|lcrcl|}\hline \text { Source of } & {\text { Sum of }} & {\text { Mean }} & \\\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\\text { Regression } & 305.1 & 1 & ? & ? \\\text { Residual } & 1247.3 & 24 & ? & \\\text { Total } & 1552.4 & 25 & & \\\hline\end{array}$

-What is a weakness of the ANOVA method compared to the t-test method when performing a significance test on the slope of a regression?

A) The ANOVA method can't test against null hypothesis slopes different from 0.
B) The ANOVA method can't use data that has outliers.
C) The ANOVA method is more prone to Type I error for data with high variance.
D) The ANOVA method is more prone to Type I error for small sample sizes.

Question 13

Consider the partially completed ANOVA table showing the results of a regression analysis shown.
?
$\begin{array}{|lcrcl|}\hline \text { Source of } & {\text { Sum of }} & {\text { Mean }} & \\\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\\text { Regression } & 305.1 & 1 & ? & ? \\\text { Residual } & 1247.3 & 24 & ? & \\\text { Total } & 1552.4 & 25 & & \\\hline\end{array}$

-If the slope is -1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the t-value we obtain when doing a t-test using a hypothesized slope of zero?

A) -0.867
B) -1.367
C) -1.867
D) -2.367

Question 14

Consider the partially completed ANOVA table showing the results of a regression analysis shown.
?
$\begin{array}{|lcrcl|}\hline \text { Source of } & {\text { Sum of }} & {\text { Mean }} & \\\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\\text { Regression } & 305.1 & 1 & ? & ? \\\text { Residual } & 1247.3 & 24 & ? & \\\text { Total } & 1552.4 & 25 & & \\\hline\end{array}$

-If the slope is -1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, based on the t-test statistic using a hypothesized slope of zero, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value?

A) P > 0.05
B) 0.02 < P < 0.05
C) 0.01 < P < 0.02
D) P < 0.01

Question 15

Consider the partially completed ANOVA table showing the results of a regression analysis shown.
?
$\begin{array}{|lcrcl|}\hline \text { Source of } & {\text { Sum of }} & {\text { Mean }} & \\\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\\text { Regression } & 305.1 & 1 & ? & ? \\\text { Residual } & 1247.3 & 24 & ? & \\\text { Total } & 1552.4 & 25 & & \\\hline\end{array}$

-If the slope is -1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, what is the t-value we obtain when doing a t-test using a hypothesized slope of 1.0?

A) -2.000
B) -2.200
C) -2.400
D) -2.600

Question 16

Consider the partially completed ANOVA table showing the results of a regression analysis shown.
?
$\begin{array}{|lcrcl|}\hline \text { Source of } & {\text { Sum of }} & {\text { Mean }} & \\\text { variation } & \text { squares } & \text { df } & \text { squares } & \text { F-ratio } \\\text { Regression } & 305.1 & 1 & ? & ? \\\text { Residual } & 1247.3 & 24 & ? & \\\text { Total } & 1552.4 & 25 & & \\\hline\end{array}$

-If the slope is -1.64, the residual mean square is 3.6, the sum of squares for X is 2.5, and the sample size is 16, based on the t-test statistic using a hypothesized slope of 1.0, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value?

A) P > 0.05
B) 0.02 < P < 0.05
C) 0.01 < P < 0.02
D) P < 0.01

Question 17

Which of the following is not an assumption of linear regression?

A) Across the entire range of the X-values, the distribution of Y-values is normally distributed around the regression line.
B) Across the entire range of the X-values, the mean of the Y-values lies on a straight line.
C) Across the entire range of the X-values, the number of Y-values is constant.
D) Across the entire range of the X-values, the variance of the Y-values is the same.

Question 18

If the assumptions of linear regression are met, then a residual plot will have all of the following features except which one?

A) The cloud of points above and below the zero line will be roughly symmetric.
B) The cloud of points above and below the zero line will have roughly the same variance.
C) The distribution of X-values will be roughly symmetric.
D) There will be no clear signs of a curved pattern throughout the range of X-values.

Question 19

What is the effect of measurement error in the Y-values?

A) Both the slope and the variance of the residuals are changed.
B) Neither the slope or the variance of the residuals is changed.
C) The slope is changed, but the variance of the residuals is not.
D) The variance of the residuals is changed, but the slope is not.

Question 20

The Michaelis-Menten equation is used to model what kind of nonlinear pattern in a data set?

A) Asymptotic increase.
B) Cyclical fluctuations.
C) Exponential growth.
D) Power law declines.

Question 21

The Michaelis-Menten equation takes the form of which of the following?

A) Y = aX / bX
B) Y = aX / (b + X)
C) Y = (a + X) / bX
D) Y = (a + X) / (b + X)

Question 22

The quadratic curve is specified by an equation like which following?

A) Y = aX^b
B) Y = ab^x
C) Y = a + bX + cX ²
D) Y = (a + bX) / cX²

Question 23

Formula-free curve fitting includes methods called "kernel," "spline," and "loess," which collectively are called ______.

A) basing
B) linearizing
C) modeling
D) smoothing

Question 24

Logistic regression predicts the ____ of occurrence of a(n) ____ variable as a function of a continuous variable?

A) distribution; integer
B) number; qualitative
C) probability; binary
D) rate; quantitative

Question 25

For a logistic regression analysis of doses of a drug (measured in mg of drug/kg body mass) in which a = -0.66 and b = 2.8, what would the LD50 be?

A) 0.118 mg/kg
B) 0.236 mg/kg
C) 2.121 mg/kg
D) 4.242 mg/kg

Question 26

The method in which quantitative statements about effect sizes from all known scientific studies are combined to generate an overall estimate is called which of the following?

A) Combo-analysis
B) Meta-analysis
C) Uber-analysis
D) Ultra-analysis

Question 27

Which of the following was not listed as a suggestion for creating data sets that can be used in subsequent meta-analyses?

A) Clearly describe conflicts of interest.
B) Provide standard errors and effect size.
C) Provide test statistics and degrees of freedom.
D) Upload data sets to an established online archive.

Question 28

The linear least squares line always goes through the point corresponding to the mean values of X and Y.

Question 29

Residuals can have either positive or negative values.

Question 30

To calculate the residual mean square, we use n-3 instead of n-1 as we would for a usual variance.

Question 31

Using extrapolation to predict Y values outside the range of X values studied is not recommended.

Question 32

Confidence bands allow us to predict the region within which 95% of the data points used in a regression will be.

Question 33

If the null hypothesis of a t-test for the slope of a regression line is true, then there is no association between the X and Y values.

Question 34

If the null hypothesis of an ANOVA test of the slope of a regression line is true, then there is no association between the X and Y values.

Question 35

The regression fallacy describes the process by which subsequent measurements will result in the slope of a relationship attenuating.

Question 36

Regression toward the mean will occur for data sets that exhibit R ²< 1.0.

Question 37

Regression analyses require that the X and Y values follow a bivariate distribution.

Question 38

Single outliers can have a dramatic effect on the slope obtained in a regression analysis.

Question 39

The log transformation works well to linearize exponential relationships but not power relationships.

Question 40

The log transformation often works well to resolve problems of unequal variance for count data.

Question 41

The effects of measurement error in the X-values and the Y-values are identical with regard to the slope of the linear regression line.

Question 42

Measurement error reduces the R².

Question 43

The Michaelis-Menten equation models exponential growth.

Question 44

The quadratic curve is used to model parabolic patterns.

Question 45

Thee null hypothesis of a logistic regression is that the probability of the occurrence of the binary variable is unrelated to the values of proposed explanatory numerical variable.

Question 46

Reporting the P-values of statistical tests is sufficient detail for most subsequent meta-analysis studies.

Question 47

Meta-analysis studies can often provide more-precise estimates of effect sizes than individual studies can.

Question 48

Consider the data set shown in the table.
​
(a) Make a graph of the data points.
(b) Calculate the slope and Y-intercept.
(c) Plot the linear least squares line on your graph.
(d) Make a second graph showing the residuals.
(e) Calculate the t-value for a significance test of the slope of your linear least squares line.
(f) Using your results from (e) make a statement about the significance of the relationship between the X and Y values.

Question 49

Consider the data set shown in the table.
​
​
(a) Make a graph of the data points.
(b) Calculate the slope and Y-intercept.
(c) Plot the linear least squares line on your graph.
(d) Make a second graph showing the residuals.
(e) Calculate the t-value for a significance test of the slope of your linear least squares line.
(f) Using your results from (e), make a statement about the significance of the relationship between the X and Y values.

Question 50

Describe when would we prefer to use the t-test procedure to test the significance of our linear least squares slope and when would we prefer the ANOVA approach.

Question 51

Using a very simplified diagram, illustrate the phenomenon of regression to the mean. Do this by drawing a set of data and then showing how it would likely change from that first measurement to the second and how this influences the slope. Annotate your diagram to make it clear what is happening.

Question 52

When and why would we transform data during a linear regression procedure?

Question 53

Draw a graph showing the data points (1, 1), (2,4), (3,9), (4,16) and then transform the data with a square root transformation on the Y-values and show those points using different symbols. Indicate which type of curve would be most appropriate to model each data set and describe what you would do if you wanted to know if the relationship between X and Y was statistically significant.

Question 54

In your own words, describe what a logistic regression is. What is the goal of a logistic regression and what do the axes in the plot represents conceptually?