Editing Logistic regression (section)

===Predictions===
The {{tmath|\beta_0}} and {{tmath|\beta_1}} coefficients may be entered into the logistic regression equation to estimate the probability of passing the exam.

For example, for a student who studies 2 hours, entering the value <math>x = 2</math> into the equation gives the estimated probability of passing the exam of 0.25:

: <math>
t = \beta_0+2\beta_1 \approx - 4.1 + 2 \cdot 1.5  = -1.1
</math>

: <math>
p = \frac{1}{1 + e^{-t} } \approx 0.25 = \text{Probability of passing exam}
</math>

Similarly, for a student who studies 4 hours, the estimated probability of passing the exam is 0.87:

: <math>t = \beta_0+4\beta_1 \approx - 4.1 + 4 \cdot 1.5  = 1.9</math>

: <math>p = \frac{1}{1 + e^{-t} } \approx 0.87 = \text{Probability of passing exam} </math>

This table shows the estimated probability of passing the exam for several values of hours studying.

{| class="wikitable"
|-
! rowspan="2" | Hours<br />of study<br />(''x'')
! colspan="3" | Passing exam
|-
! Log-odds (''t'') !! Odds (''e<sup>t</sup>'') !! Probability (''p'')
|- style="text-align: right;"
| 1|| −2.57 || 0.076 ≈ 1:13.1 || 0.07
|- style="text-align: right;"
| 2|| −1.07 || 0.34 ≈ 1:2.91 || 0.26
|- style="text-align: right;"
|{{tmath|\mu \approx 2.7}} || 0 ||1 || {{sfrac|1|2}} = 0.50
|- style="text-align: right;"
| 3|| 0.44 || 1.55 || 0.61
|- style="text-align: right;"
| 4|| 1.94 || 6.96 || 0.87
|- style="text-align: right;"
| 5|| 3.45 || 31.4 || 0.97
|}