Suppose that we have a dataset of heights and weights for 100 adults. We fit a linear regression and print the coefficients:

model = sm.OLS.from_formula('weight ~ height', data = body_measurements) results = model.fit() print(results.params)

Output:

Intercept -21.67 height 0.50 dtype: float64

This regression allows us to predict the weight of an adult if we know their height. To make a prediction, we need to plug in the intercept and slope to our equation for a line. The equation is:

`$weight = 0.50*height - 21.67$`

To make a prediction, we can plug in any height. For example, we can calculate that the expected weight for a 160cm tall person is 58.33kg:

`$weight = 0.50*160-21.67 = 58.33$`

In python, we can calculate this by plugging in values or by accessing the intercept and slope from `results.params`

using their indices (`0`

and `1`

, respectively):

print(0.50 * 160 - 21.67) # Output: 58.33 # OR: print(results.params[1]*160 + results.params[0]) # Output: 58.33

We can also do this calculation using the `.predict()`

method on the fitted model. To predict the weight of a 160 cm tall person, we need to first create a new dataset with `height`

equal to `160`

as shown below:

newdata = {"height":[160]} print(results.predict(newdata))

Output:

0 58.33 dtype: float64

Note that we get the same result (`58.33`

) as with the other methods; however, it is returned as a data frame.

### Instructions

**1.**

In **script.py**, you’ll see the code (from the previous exercise) to fit a model that predicts test `score`

using `hours_studied`

. Print the coefficients of this model using `.params`

.

**2.**

Using your model, what is the predicted score for a student who spent 3 hours studying? Save the result as `pred_3hr`

and print it out. Calculate your answer by plugging into the formula for a line (instead of using `.predict()`

).

**3.**

What is the predicted score for a student who spent 5 hours studying? Use the `.predict()`

method to calculate your answer and save it as `pred_5hr`

, then print it out.