Question

With linear regression, intercept = 10.06 & coefficient = 0.5. With logistic regression, intercept = 5.87 & coefficient = 0.2. Which of the following is True?

  1. If using linear regression, one unit increase in X is associated with an increase in Y by 0.5
  2. If using logistic regression, one unit increase in X is associated with an increase in Y by 0.2.

Answer

Only first statement is true.

With linear regression: \[y = \beta_0 + \beta_1*x\] And its given that \(\beta_0 = 10.06\) and \(\beta_1 = 0.5\). So, \[y = 10.06 + 0.5*x\] So if \(x\) is increased by 1, then \(y\) increases by 0.5

With logistic regression: \[log(\frac {p(y)}{1-p(y)}) = \beta_0 + \beta_1*x\] And it is given that \(\beta_0 = 5.87\) and \(\beta_1 = 0.2\). So \[log(\frac {p(y)}{1-p(y)}) = 5.87 + 0.2*x\] So if \(x\) is increased by 1, the probability of \(y\) is going to increase. A one unit increase \(x\) is associated with an increase in log odds of \(y\) by 0.2.

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