Statistics: Regressions and associations

Question 1

What does the b in the line equation represent

Answer 1

The slope equals the amount that y changes when x increases by one unit.

Question 2

What is the function of the absolute value of the slope?

Answer 2

Describes the magnitude of the change in y^ for 1 unit change in x, the larger it is the steeper the slope

Question 3

What is meant by prediction error? Give another word for these

Answer 3

The difference between the actual y value and the predicted y value. These are also known as residuals.

Question 4

When is it a positive residual

Answer 4

When the actual y is larger than the predicted y

Question 5

What is meant by the least squares method?

Answer 5

This chooses the best possible regression line that has the smallest value of the residual sum of squares.

Question 6

Apart from making errors small as possible name two characteristics of the regression line

Answer 6

• Has positive and negative residuals

- passes through the mean point

Question 7

Why can’t we just use a slope to measure correlation

Answer 7

Different units of measurement for the variables

Question 8

Name two connections between correlations and regressions

Answer 8

• They are both appropriate when the relationship between two quantitative variables can be approximated by a straight line
• The correlation and the slope of the regression line have the same sign. If one is positive, so is the other one.

Question 9

Name three key differences between regression and correlation

Answer 9

With regression you must identify explanatory and response variables as this will affect the direction of the slope, this is not the case with correlation. The regression line also depends on the measurement units. Finally the correlation falls between -1 and 1 while the slope can take on any figure.

Question 10

What is the typical way to interpret r^2

Answer 10

The proportion of the variation in the y-values that is accounted for by the linear relationship of y with x.

Question 11

Name 4 pitfalls of association analysis

Answer 11

Extrapolation (using a regression line to predict y values for x values outside of the range of data)
Influential regressive outliers
Implying causality
lurking variables

Question 12

What two conditions are required for an outlier to be influential

Answer 12

• x value is relatively loe or high compared to the rest of the data
• Falls far from the trend that the rest of the data follows (regression outlier)

Question 13

What are predictions of the future using time series data called

Answer 13

forecasts

Question 14

What is meant by non resistant in data

Answer 14

prone to distortion by outliers

Question 15

What is meant by a lurking variable?

Answer 15

One that influences the association between two other variables

Question 16

What is the simpson’s paradox

Answer 16

When a trend appears in several different groups on data but disappears or reverses when these groups are combined

Question 17

When does confounding occur?

Answer 17

When two explanatory variables are both associated with a response variable but are also associated with each other

Question 18

Whats the difference in a lurking and confounding variable?

Answer 18

a lurking variable is not measured in the study