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

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2
Q

Correlations

A
  • between +1 and -1
  • strength and directionality
  • correlation = covariance (x,y) / SD(x) x SD(y)
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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.
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4
Q

Regression line and correlations

A
  • R and the slope will always have the same line.
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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??
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6
Q

Influential points

A
  • outliers that can have an effect on the data.
  • lurking variables: neither explanatory nor response but influences interpretation.
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7
Q

Cause and effect relationship

A
  • experimental designs only.
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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.
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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
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10
Q

T-test for the slope

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

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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
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13
Q

Variables

A

Explanatory variables influence the outcome (response variables)

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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.
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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.
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16
Q

Residuals

A

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.

17
Q

Extrapolation

A

Making predictions outside of a given range

18
Q

Correlation vs causation

A
  • 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.