Biostats Lesson 7

The​​ (a)   is the Dependent variable or the variable being observed.

The​ (b)   is the Independent variable or the variable being manipulated.

• x
• y

The residual (e_i) is the​ (a)   value (y_i) minus the ​ (b)   value (ŷ_i).

• observed
• predicted
• mean

Outlier: An observation that is extremely different from other observations.

Influential point: A point in the data that would have a significant impact on the life of best fit if removed.

Given the above definitions, is this statement true or false: all outliers are influential points.

• True

• False

Answer explanation

You can have an outlier without it being an influential point. The first outlier in the image is an influential point while the second outlier in the image is not.

Select ALL TRUE statements about the coefficient of determination (r²).

• Number between 0 and 1.

• The closer it is to 0, the better our least-squares regression line explains the response.

• Proportion of variation in y.

• Correlation between y and x.

• The closer it is to 1, the better our least-squares regression line explains the response.

Match the following variables with what they represent.

• Slope

• ȳ / x̄

• Correlation

• a

• Intercept

• r

• Standard Deviation

• b

• Mean

• S_x / S_y

Select the r² value that would belong to the best fitting least-squares regression line.

• 0.03

• 0.48

• 0.96

Answer explanation

The closer r² is to 1, the better the line fits. 0.96 is the closest value to 1.

Which example from the image is most impacted by the outlier represented in red?

• Example 1

• Example 2

• Example 3

T/F: You need the mean of x and the mean of y OR the slope of your least-squares regression line to find ŷ.

• True

• False

Answer explanation

You need both of these things to find ŷ.

To find the slope (b) in your equation, you must first find:

(select all correct answer options)

• Correlation between x and y (r).

• Standard deviation of x (S_x).

• Standard deviation of y (S_y).

• y-intercept (a).

• Sample mean (ȳ).

Answer explanation

T/F: If b is negative then r is negative.

• True

• False

Answer explanation

The slope and the correlation will always have the same sign.