Further Techniques in Multiple Linear Regression Flashcards

1
Q

What does linear regression assume?

A

That an independent predictor variables and the outcome dependent variable are related linearly.

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2
Q

How do we fix a non linear regression model?

A
  • By transforming the variables in the model
  • By fitting polynomial relationship instead of a straight line
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3
Q

How does polynomial fitting work?

A
  • The principle of fitting a straight line applies, but we are just turning one predictor variable into two or more
  • Instead of predicting y on x, we predict y on x, and x^2 (and possibly x^3, x^4, etc)
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4
Q

List an advantage of polynomial fitting.

A

Allows us to deal with obvious non-linear relationship without having to specify in advance what the appropriate transformation would be

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5
Q

How do we fit a quadratic model?

A
  • We transform x to x^2
  • y = β(0)+ β(1)x+ β(2)x^2 + e
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6
Q

How do we interpret quadratic terms?

A
  • Where x > 0 and x^2 < 0, y is increasing in x at first, but will eventually turn around and be decreasing
  • Where x < 0 and x2 > 0, y is decreasing in x at first, but will eventually turn around and being increasing
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7
Q

What is an advantage of transformed data?

A
  • Often less skewed
  • Outliers are less extreme
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8
Q

List three examples of transformed data.

A
  • Logarithms
  • Inverse
  • Square root
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9
Q

What is an interaction effect?

A

When the effect of an explanatory variable depends on the level of another explanatory variable.

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10
Q

Give an example of an interaction effect.

A
  • Assume male happiness increases with years of marriage, whereas females happiness decreases with years of marriage
  • The relationship between happiness and years of marriage may be linear, but it would not be independent of sex.
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11
Q

Write the regression equation of a model with interaction terms.

A

y = β0+ β(1)x^1+ β(2)x^2+ β(3) (x(1)x(2)) + e
where β3 (x1x2) is a multiplicative term of the two main effects

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12
Q

What is the most common centring method?

A

Mean centring

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13
Q

How can we ensure B(0) is interpretable?

A

By changing x by centring the age variable.

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14
Q

What changes when you carry out mean centring?

A

The intercept which now corresponds to the average age, e.g. x(centred), not x=0

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15
Q
A
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