Correlation And Regression

Question 1

Regression line

Answer 1

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

Question 2

Correlations

Answer 2

• between +1 and -1
• strength and directionality
• correlation = covariance (x,y) / SD(x) x SD(y)

Question 3

Coefficient of determination

Answer 3

• 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.

Question 4

Regression line and correlations

Answer 4

• R and the slope will always have the same line.

Question 5

Least squares regression line

Answer 5

• 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??

Question 6

Influential points

Answer 6

• outliers that can have an effect on the data.
• lurking variables: neither explanatory nor response but influences interpretation.

Question 7

Cause and effect relationship

Answer 7

• experimental designs only.

Question 8

SPSS output

Answer 8

• Constant = slope
• BTU (name of variable) = intercept.
• interpretation: for every x input, the output increases by the amount of the intercept.

Question 9

Distributions

Answer 9

• 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

Question 10

T-test for the slope

Answer 10

• degrees of freedom: n - p - 1 (p = # of predictors)

Question 11

Multiple regression line

Answer 11

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)

Question 12

Confidence interval

Answer 12

• 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

Question 13

Variables

Answer 13

Explanatory variables influence the outcome (response variables)

Question 14

Regression coefficients

Answer 14

• estimates of the unknown population parameters and describes the relationship between predictor and response.
• coefficients are the values that multiply the predictor values.

Question 15

F test

Answer 15

• 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.

Question 16

Residuals

Answer 16

Observerd value - predicted value
- positive = values are being underpredicted.
- negative = values are being overpredicted
- values are positive when over the regression line and negative when under.

Question 17

Extrapolation

Answer 17

Making predictions outside of a given range

Question 18

Correlation vs causation

Answer 18

• causation: x influences y, y influences x
• common response: x influences y, y influences x but z influences x and y.
• confounding: x influences y, y influences x but z influences y and x and z influence each other too.