Flashcards
RMD lecture 6
Cards in this deck (36)
- 1what does a correlation coefficient of r=.04 tell you?there is a negative correlation
- 2which of the following is the weakest correlation? r=.99 r=.15 r=.09 r=.21 r=.75A: r=.09
a negative correlation is not a weak correlation - this is the direction - 3How much variance/variability in the data can a relationship with a coefficient .6A; 36%
.6 time . = .36 - 4what is the purpose of linear regression?discover the effect of one variable (which we denote by x ) on another (which we denote by y ).
while correlational analysis allows us to conclude how strongly two variables relate to each other (both magnitude and direction), linear regression will answer the question &;By how much will y change, if x changes; In other words, if x changes by a certain amount, we will be able to estimate how much y will change. - 5diet coke exampleImagine we have data on the amount of diet cola bought and the price of diet cola. Now, if the price of diet cola becomes high enough, the sales of diet cola will decrease (people will swap to a cheaper alternative). A simple correlational analysis will show us that the price of diet cola and sales of diet cola are negatively correlated ; we are able to say, then, that as the price increases, sales decrease. But we cannot tell by how much sales will decrease, for any given price rise. Psychologists use linear regression in order to be able to assess the effect that x has on y .
- 6what is the variable that is being predicted?The variable that is being predicted is called a criterion or dependent variable (DV). This is also called y .
- 7What is the name of the variable that is predicting the DV?The variable that is predicting the DV is, not surprisingly, called the predictor (or explanatory ) variable (IV); this is also called x .
- 8—12.1, that there is a positive correlation between x and y (actually + 0.9), but all you can say at this point is that, as marks in the mock exam increase, marks in the final exam increase. The dots cluster quite tightly around an imaginary line, but how can we predict a person’s final mark from his or her marks in the mock exam? The answer, of course, is linear regression. Linear regression is a method by which we fit a straight line to the data. This line is drawn in the best place possible – that is, no other line would fit as well. This is why it is called the line of best fit ; we talk about this more in the following paragraphs (see Figure 12.2).
- 9drawing the line-the line is called a model - model of the data
- with high correlation line models correlation quite well - 10what is the regression line also known as?known as the line of best fit
the closest we can make it to all the data points - 11what can be said about curve relationships?-systematic relationships
-cant use linear regression on this
- may feel somewhere in the middle - 12—Every time x increases by 1, y increases by 10. (Make sure you confirm this by looking at Figure 12.3.) The 0 is where the line intersects the y -axis. This means that, when a person scores 0 on x , they score 0 on y too.
- 13regression equationwhen we perform a linear regression analysis, we obtain a regression equation, which shows the way in which y changes as a result of change in x . From this formula, we can calculate someones score on y from their score on x . The general formula looks like this:
y=a+bx
or
y=bx+a - 14how can y be predictedy can be predicted by a value denoting the slope of the line multiplied by their particular score on x , added to a value denoted by a
- 15what do the individual sections of the regression mean?y is the variable to be predicted
x is the score on the variable x
b is the value for the slope of the line
a is the value of the constant: that is, the place where the straight line intercepts the y -axis (also called the intercept). - 16residualswe use our line of best fit to predict a persons score, unless we have a perfect relationship we will always make some errors.
If our line of best fit is really good for predicting, then the differences between the actual and predicted figures will be small; if the line of best fit is not good at predicting, then the differences will be large. The differences between the actual scores and predicted scores are called residuals . - 17explain the interceptthe expected value of Y when the value of X is equal to zero
- 18what does this figure show?In Figure 12.6, the line has started at 5. (This means that a person who has scored 0 on x would be predicted to score 5 on y . Of course, sometimes it would be impossible to score 0 on x; if x were IQ, for instance. For every value of x , y increases by 5. So the formula you need in order to predict is:
x were IQ, for instance. But we won’t worry about this for now!) For every value of x , y increases by 5. So the formula you need in order to predict is:
x were IQ, for instance. But we won’t worry about this for now!) For every value of x , y increases by 5. So the formula you need in order to predict is:
y = 5 + 5 x
If a person has a score of 3 on x , the predicted score on y will be:
y= 5 (5 *3) = 20
- 19What is the slope?The expected increase or decrease in the DV as a function of an increase or decrease in the IV
- 20what does prediction tell us?prediction cant tell us everything that is going one.
Error - work out what predicted y is for each person - compare to actual y
take actual value and take way the predicted - 21what happens if you add up all the residuals?if you add up all the residuals you will get 0
- 22what happens if you square the residuals?if you square the residuals you will get an idea of how close the fit is
- 23what are three steps for running the linear regression?1. Explore the data: normally distributed? - avoid using a kilmogrov smirnov
2: scatterplot: assumptions met? - check if they a broadly linear
3. Run the linear regression analysis - 24why do we want the scatter t be homoscedastic?- dont want the data to be spread more at some point along x.
Y is normal at all values of X
Y 's spread is the same at all values of X - 25what is leverage?distance from the mean
- 26what is error?distance from regression line
- 27outliers have the largest effect when...error is high
leverage is high - 28—you must report the correlation for multiple regression
r = -.896, N = 12, p < .001- correct statistical description
- 29—this table can show you one predictor at a time
this is the descriptions of the model
time on Facebook is the
the criterion can be seen below (RMD exam performance)
- 30—the model summary is a mathematical description of the variance the model can account for
- 31—ANOVA of linear regression is the same thing
- use to check if our regression is significant
get something that looks like a one way ANOVA
F(1, 10) = 40.858, p < .001 - overall significance
- 32—Regression equation: y = a + bx
y = 102.039 -1.478x
coefficients give us an idea of how good predictors are
the beta is useful for looking at more than one predictor
- 33regression and individualsA prediction about an individual
is not necessarily true
But we can replace an expensive test with a cheap
predictor and then screen lots of people
We can then use the predictions
to decide who to give the real test to
- may pot be good for one person
- but tend to be true for a sample - 34what are the limits of prediction?If you don't collect the right data, may end up coming to the wrong conclusions
- 35aintercept - when the regression line crosses the y axis
- 36bXslope - is the angle in which the line is fitted
Information
- Description
- Flashcards on RMD lecture 6, created by Toyin O on 05/03/2018.
- Created by
- Toyin O
- Views
- 2
- Rating