Lecture 9 - Correlation & Regression

Question 1

In a binary relationship, what are x and y ?

Answer 1

x = explanatory variable
y = response variable

Question 2

Give an example of a response variable that you cannot put on y axis bc it is dichotomous (yes/no) ?

Answer 2

x = smoking
y = lung cancer

*can’t use lung cancer bc it’s either yes or no

Question 3

A scatter plot can only be used when both variables are _______

Answer 3

numerical

Question 4

How can you describe the overall pattern of a scatterplot ?

Answer 4

by the form, direction, and strength of the relationship between the data

Question 5

Describe the form and direction of the relationship

Answer 5

• Linear relationships, where the points roughly follow a straight line, are especially important.
• Relationships can be negative (A) or positive (B) in direction.
• Curvilinear relationships (C) and clusters (D) are other things to watch for.
• An important kind of deviation is an OUTLIER (E) where an individual value that falls outside the overall pattern

Question 6

The strength of a relationship is determined by ??

Answer 6

how close the points in the scatter plot lie to a simple form such as a line

Question 7

We use the _____ to evaluate the variability for univariate data; where n is the sample size

Answer 7

variance

Question 8

For bivariate data, we use the _______ (the variance in x & y ) where n is the number of x,y pairs.

Answer 8

covariance

Question 9

The covariance is limited as ?

Answer 9

a tool for measuring and describing relationships because it’s composite units are difficult to translate

Question 10

Standardized values of variance have ____ units.

Answer 10

no (they are the same whether x is measured in cm or mg)

Question 11

What do standardized values express?

Answer 11

Their deviations from the mean in terms of their s, and avoid the problem of trying to interpret unit-dependent covariance units.

Question 12

What is the correlation coefficient ?

Answer 12

The strength of a relationship is quantified by the standardized covariance of the two continuous measures, which is termed the correlation coefficient p (rho) or more formally as the Pearson correlation coefficient.

The sample correlation coefficient is r

Question 13

What does the correlation coefficient measure?

Answer 13

It measures both the strength and direction of a linear relationship between 2 continuous variables.

Question 14

What is the square of the correlation coefficient?

Answer 14

r^2 is referred to as the coefficient of determination

Question 15

When are two variables x and y positively associated ?

Answer 15

when above-average values of one variable tend to go with above-average values of the other; in this case r will be positive

Question 16

When are two variables x and y negatively associated ?

Answer 16

when above-average values of one variable tend to go with below-average values of the other; in this case r will be negative

Question 17

For the correlation coefficient, what is the null and alternative hypothesis ?

Answer 17

Null hypothesis: p = 0 (There is no linear relationship

Alternative hypothesis: p does not = 0 (Height and weight are linearly related)

**We can evaluate the correlation, using alpha = 0.05 with degrees of freedom n-2

Question 18

Correlation makes no distinction between ______ and ______ variables.

Answer 18

explanatory and response

Question 19

Correlation requires both variables to be _____

Answer 19

numerical

Question 20

Correlation does not depend on the scale of ______ used

Answer 20

measurement

Question 21

r > 0 indicates ?

Answer 21

a positive relationship between the variables

Question 22

r < 0 indicates ?

Answer 22

a negative relationship between the variables

Question 23

Correlation is always between ?

Answer 23

-1 and 1

Question 24

Correlation measures the strength of linear relations and doesn’t apply to ____ relations

Answer 24

curved

Question 25

Like the mean and SD, the correlation is strongly affected by ______

Answer 25

outliers

Question 26

correlation coefficient can become a ____-tailed test

Answer 26

one

Question 27

Correlation coefficient test" | Degrees of freedom ?

Answer 27

n-2

Question 28

Compare regression to correlation

Answer 28

With correlation, we capture the degree to which to variable co-vary, there is no question about casual relationships With regression, we introduce the concept of dependent and independent variables

Question 29

What is the task in regression?

Answer 29

to find some meaningful way of describing the essence of a dependent relationship

Question 30

Regression extends the concept of ______ by summarizing the relationship between 2 variables with a straight line that best describes their relationship. This line is termed the regression line.

Answer 30

correlation

Question 31

dependent variable is always presented as the __-variable and is always plotted on the _____ axis of the regression plot

Answer 31

y, vertical

Question 32

The independent variable __ is plotted on the _______ axis

Answer 32

x, horizontal

Question 33

To describe the regression line we need to know two values, what are they?

Answer 33

1) The slope "b". - This value has clear practical interpretation, such as the average increased response per increase in dose. 2) The y-intercept "a". - This may have a practical interpretation (such as HR at rest); in some cases it may not ex. the weight of all individual with zero height ?????

Question 34

what is Y-claret ?

Answer 34

The predicted value.

Question 35

The fit of the predicted value can be summarized by ?

Answer 35

the difference between the value y observed, and the value of y (y-claret) predicted by the regression line. The difference is called the residual value!! y - y(claret) = observed - predicted

Question 36

What is the formula for SSE?

Answer 36

sum of square of the error SSE = sum of [(y-y^) squared]

Question 37

When you find the y intercept, what are you testing for? (slide 50)

Answer 37

solving for b testing to see if it's a negative or positive relationship

Question 38

Having obtained the regression line, we need to establish that it's predictive value has not arisen by _____ alone.

Answer 38

chance

Question 39

If b = 0, what does that mean?

Answer 39

there is no correlation between x and y (LIKE AT ALL)

Question 40

For regression, what is the null and and alternative hypothesis ? *this test is similar to ANOVA

Answer 40

Null: B = 0 Alternative: B does not = 0 *We still use F test, just like ANOVA

Question 41

We find SST which is ?

Answer 41

SSR + SSE

Question 42

df = ?

Answer 42

(SSR) Explained: df = 1 (SSE) Error: df = n-2 (SST) Total: df = n-1

Question 43

How do we calculate r^2?

Answer 43

r^2 = SSR (explained) / SST (total)