# Lesson 7

Confident Models

- Let’s explore our confidence in linear models.

### 7.1: Math Talk: Ordering Decimals

Mentally order the numbers from least to greatest.

20.2, 18.2, 19.2

-14.6, -16.7, -15.1

-0.43, -0.87, -0.66

0.50, -0.52, 0.05

### 7.2: Ranking Models

- Here are scatter plots that represent various situations. Order the scatter plots from “A linear model is not a good fit for the data” to “A linear model is an excellent fit for the data.”
- Here are two scatter plots including a linear model. For each model, determine the \(y\) when \(x\) is 15. Which model prediction do you think is closer to the real data? Explain your reasoning.

### 7.3: Predicting Value

Here are situations represented with graphs and lines of fit. Use the information given to complete the missing fields for each situation.

- The model predicts how much money, in dollars, the coach will make based on how many athletes sign up for one-on-one training. The model is represented with the equation \(y=200 + 25x\).
- The slope of the model is \(\underline{\hspace{.5in}}\) (positive or negative).
- What does the model predict would be the amount the coach makes when there are 10 athletes present?
- Using the data points and the model as a reference, what is a reasonable range of money the coach will make when there are 10 athletes present?
- This model is a \(\underline{\hspace{.5in}}\) (great, good, okay, or bad) fit for the data.
- Using numbers between 0 and 1, rate your confidence in the model where 0 is no confidence and 1 is total confidence.

- The model predicts the annual salary of a worker in a certain government position based on years of experience. The model is represented with the equation \(y=1.5x + 35\).
- The slope of the model is \(\underline{\hspace{.5in}}\) (positive or negative).
- What does the model predict would be the employee’s salary when the employee has 10 years of experience?
- Using the data points and the model as a reference, what is a reasonable range for the salary of a worker based on 10 years of experience?
- This model is a \(\underline{\hspace{.5in}}\) (great, good, okay, or bad) fit for the data.
- Using numbers between 0 and 1, rate your confidence in the model where 0 is no confidence and 1 is total confidence.

- The model predicts the number of absences a school will have based on the number of incentives given per month. The model is represented with the equation \(y= \text-2.18x + 54.78\).
- The slope of the model is \(\underline{\hspace{.5in}}\) (positive or negative).
- What does the model predict would be the number of absences when 10 incentives are given for the month?
- Using the data points and the model as a reference, what is a reasonable number of absences when there are 10 incentives given?
- This model is a \(\underline{\hspace{.5in}}\) (great, good, okay, or bad) fit for the data.
- Using numbers between 0 and 1, rate your confidence in the model where 0 is no confidence and 1 is total confidence.