You are given a model with age as an independent variable, and you run the following line of code:

```
1 - pchisq(964.52 - 960.23, 713 - 712)
```

This results in 0.038.

**Coefficients:**

| Estimate | Std. Error | z value | Pr(>|z|) |
|----------|------------|---------|---------|
| (Intercept) | -0.05622 | 0.17353 | -0.327 | 0.7438 |
| Age | -0.01006 | 0.00533 | -2.057 | 0.0397 |

**Question:**

What is your best guess of the probability of "Survived" being equal to 1 if your alpha value is 0.012?

You are modeling whether an individual is going to survive the Titanic disaster.

The first 6 rows are as follows:

| PassengerId | Survived | Class | Name | Sex | Age | SibSp | Ticket |
|-------------|----------|-------|----------------------------------------------------|--------|-----|-------|----------------|
| 1 | 0 | 3 | Braund, Mr. Owen Harris | male | 22 | 1 | A/5 21171 |
| 2 | 1 | 1 | Cummings, Mrs. John Bradley (Florence Briggs Thayer) | female | 38 | 1 | PC 17599 |
| 3 | 1 | 3 | Heikkinen, Miss. Laina | female | 26 | 0 | STON/O2. 3101282 |
| 4 | 1 | 1 | Futrelle, Mrs. Jacques Heath (Lily May Peel) | female | 35 | 1 | 113803 |
| 5 | 0 | 3 | Allen, Mr. William Henry | male | 35 | 0 | 373450 |
| 6 | 0 | 3 | Moran, Mr. James | male | 0 | 0 | 330877 |

**Part (i):**

If degrees of freedom were not an issue, give one variable which would allow you to explain all of the variability in "Survived."

**Part (ii):**

Use the output below to predict the probability of survival for:

**Coefficients:**

| Estimate | Std. Error | t value | Pr(>|t|) |
|-------------|------------|---------|--------------|
| (Intercept) | 0.96809 | 0.03919 | 24.700 | < 2e-16 |
| factor(Class)2 | -0.04703 | 0.05862 | -0.802 | 0.42256 |
| factor(Class)3 | -0.46809 | 0.05039 | -9.290 | < 2e-16 |
| Sex: Male | -0.59923 | 0.05215 | -11.400 | < 2e-16 |
| factor(Class)2:Sex: Male | -0.16441 | 0.07718 | -2.130 | 0.03342 |
| factor(Class)3:Sex: Male | 0.23468 | 0.06433 | 3.648 | 0.00028 |

Note that the model above includes interaction effects, which work just like in regular regression. These effects are created by multiplying the values of the independent variables.

**Predict for:**

1) A female individual who is in second class.
2) A female individual who is in third class.
3) A male individual who is in first class.

**Confusion Table:**

| | Predicted 0 | Predicted 1 |
|---------------|-------------|-------------|
| Actual 0 | 40 | 10 |
| Actual 1 | 15 | 25 |

**Additional Information:**

- Table(Survived):
- Survived 0: 549
- Survived 1: 342

- GLM Output:
- Null deviance: 1186.70 on 890 degrees of freedom
- Residual deviance: 1084.40 on 889 degrees of freedom

**Tasks:**

a) Which of the above independent variables would you use if you wanted to predict the "Survived" variable? Justify your choice.

b) Find Sensitivity (\(P(Y_{\text{Predicted}} = 1 | Y_{\text{Actual}} = 1)\)). Show work.

c) Find Precision (\(P(Y_{\text{Actual}} = 1 | Y_{\text{Predicted}} = 1)\)). Show work.

d) Find Accuracy. Show work.