Correlation And Regression Flashcards
1
Q
Regression line
A
Y = b1 + b0x
- b1 = slope
- b0 = intercept
- predictions are based on the average.
- changes in y as the value of x goes up.
- if curved = cannot make predictions
2
Q
Correlations
A
- between +1 and -1
- strength and directionality
- correlation = covariance (x,y) / SD(x) x SD(y)
3
Q
Coefficient of determination
A
- R^2
- strength only
- explained variance - shows how well the data fits the regression model
- value ranges from 0 to 1 with 0.9 showing a good fit.
4
Q
Regression line and correlations
A
- R and the slope will always have the same line.
5
Q
Least squares regression line
A
- minimizes the sum of squares of the residuals
- residual = observed value - predicted value
- always passes through the mean of x and y
- if r = 0, then LSR = 0.
- the mean is always 0??
6
Q
Influential points
A
- outliers that can have an effect on the data.
- lurking variables: neither explanatory nor response but influences interpretation.
7
Q
Cause and effect relationship
A
- experimental designs only.
8
Q
SPSS output
A
- Constant = slope
- BTU (name of variable) = intercept.
- interpretation: for every x input, the output increases by the amount of the intercept.
9
Q
Distributions
A
- joint distribution: dividing the count in each cell by the total number of all observations
- marginal distribution: row total / column total
- conditional distribution: cell / column total
10
Q
T-test for the slope
A
- degrees of freedom: n - p - 1 (p = # of predictors)
11
Q
Multiple regression line
A
Y = b0 + b1x1 + ei
- b0 = mean(y) - b1 x mean(x)
- b1 = r(sy/sx)
- ei sums to 0 (residuals / vertical deviations from the least squared line)
12
Q
Confidence interval
A
- narrow in the middle and wider at the end
- check if its 5% (90%) in each tail or 5% total (95%)
- if 0 is in the confidence interval => cannot reject h0
- if 0 is not in the confidence intervals => intercept of the line i not 0.
- for 99% = p-value needs to be less than 0.01 to reject the null
13
Q
Variables
A
Explanatory variables influence the outcome (response variables)
14
Q
Regression coefficients
A
- estimates of the unknown population parameters and describes the relationship between predictor and response.
- coefficients are the values that multiply the predictor values.
15
Q
F test
A
- MSM is the same as MSR in formula sheet
- 2 degrees of freedom: p - 1 for numerator (model) and n - p for denominator (error). p is number of predictors and n is number of observations.
- critical value for F = find df and find critical value using the value and alpha level.
