Lecture 6 Conceptual Short-Answer

Question 1

Why do researchers often prefer reporting correlations over covariances when describing association between 2 quantitative variables?

Answer 1

As its value ranges from -1 to 1, the size of the correlation coefficient is interpretable, unlike covariance

Question 2

What does the correlation coefficient represent?

Answer 2

It is the magnitude and direction of the linear relationship between 2 variables

Question 3

How can two variables be associated but have zero correlation?

Answer 3

Correlation only measures the linear relationship, if the variables are nonlinearly related, their correlation may be 0

Question 4

Compare correlation with regression. What do they have in common, and how are they different?

Answer 4

Correlation describes the direction and strength of a linear relationship (general and without units) and produces a correlation coefficient.
Regression describes the relationship between the 2 variables by a line function with 2 model parameters (slope and intercept).
Both are used to examine the relationship between 2 variables, but provide different types of information.

Question 5

What is the goal of regression analysis?

Answer 5

To assess the relationship between 2 variables by explaining or predicting one variable using another

Question 6

In what sense can the mean be considered a good summary statisic?

Answer 6

The sample mean of a variable minimizes the sum of squared residuals for that variable when no information about other variables is available

Question 7

What does Anscombe (1973)’s quartet imply?

Answer 7

It’s good to visually look at the data, not just the statistics

Question 8

What graphs do you use for a relationship between 2 categorical variables?

Answer 8

Two-way contingency table, grouped bar graph

Question 9

What graph do you use for a relationship between 1 categorical and quantitative variables?

Answer 9

Grouped box-and-whisker plot

Question 10

What graph do you use for a relationship between 2 quantitative variables?

Answer 10

Scatterplot

Question 11

How do you find the slope in a linear regression model?

Answer 11

S(dx)(dy) / S(dx)^2

Question 12

How do you find the intercept in a linear regression model?

Answer 12

Y_bar - slope(x_bar)

Question 13

How do you calculate the residual?

Answer 13

Residual = actual - expected