Let's go through this step-by-step:

a) Calculate the linear regression model for $W$ (weight in ounces) as a function of $t$ (days).

The data points we have are:

To calculate the regression line $W = mt + b$ (where $m$ is the slope and $b$ is the y-intercept), I will apply linear regression using the given points.

Let me compute that for you.The linear regression model for $W$, based on the data, is:

$W = 2.63t + 45.94$

where:

• $m = 2.63$ is the slope (rate of weight gain per day),
• $b = 45.94$ is the y-intercept (initial weight at day 0).

b) When could you go home (i.e., weigh 80 ounces)?

To find the day $t$ when your weight reached 80 ounces, we use the equation: $80 = 2.63t + 45.94$ Solving for $t$.According to the model, you would have been allowed to go home on day 13.

c) Predicted weight on day 24

Now, let's use the model to predict your weight on day 24. We substitute $t = 24$ into the equation: $W = 2.63(24) + 45.94$According to the model, your predicted weight on day 24 would have been 109 ounces.

Would you like any further details or explanations?

Here are 5 related questions you can explore:

1. How would the model change if more data points were added?
2. What does the slope represent in this context, and why is it important?
3. Can a quadratic or another type of regression model better fit the data?
4. What are some factors that could cause deviations from the predicted model in real life?
5. How can you determine the accuracy of this regression model?

Tip: In statistics, checking the residuals of a regression model helps assess how well the model fits the data!