Use the same data sets as Exercises 13-28 in Section 10-1....

Use the same data sets as Exercises 13-28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor $(x)$ variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 484. Using the listed actress/actor ages, find the best predicted age of the Best Actor given that the age of the Best Actress is 54 years. Is the result reasonably close to the Best Actor's (Eddie Redmayne) actual age of 33 years, which happened in 2015, when the Best Actress was Julianne Moore, who was 54 years of age? $$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { Best Actress } & 28 & 30 & 29 & 61 & 32 & 33 & 45 & 29 & 62 & 22 & 44 & 54 \\ \hline \text { Best Actor } & 43 & 37 & 38 & 45 & 50 & 48 & 60 & 50 & 39 & 55 & 44 & 33 \\ \hline \end{array}$$

Use the same data sets as Exercises 13-28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor $(x)$ variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 484.
Using the listed actress/actor ages, find the best predicted age of the Best Actor given that the age of the Best Actress is 54 years. Is the result reasonably close to the Best Actor's (Eddie Redmayne) actual age of 33 years, which happened in 2015, when the Best Actress was Julianne Moore, who was 54 years of age?
$$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline \text { Best Actress } & 28 & 30 & 29 & 61 & 32 & 33 & 45 & 29 & 62 & 22 & 44 & 54 \\
\hline \text { Best Actor } & 43 & 37 & 38 & 45 & 50 & 48 & 60 & 50 & 39 & 55 & 44 & 33 \\
\hline
\end{array}$$

Key Concepts

Simple Linear Regression

This concept involves modeling the relationship between a predictor variable (independent variable) and a response variable (dependent variable) using a straight line. The equation of this line, typically written as y = b0 + b1*x, summarizes the linear association between variables, where b1 is the slope and b0 is the intercept.

Least Squares Method

The least squares method is a statistical technique used to estimate the parameters of the linear regression equation. It works by minimizing the sum of the squared differences (residuals) between the observed values and the values predicted by the linear model, ensuring the best possible fit of the line to the data.

Prediction Using the Regression Equation

This involves using the derived regression equation to estimate the value of the response variable for a given value of the predictor variable. By substituting a specific predictor value into the regression equation, one obtains the predicted response, which serves as an estimate based on the observed relationship in the data.

Model Interpretation and Validation

After calculating the regression equation and making predictions, it is important to interpret the results by comparing the predicted values with actual observations. This step helps in assessing the model's accuracy and reliability, providing insights into how closely the model's predictions match the real-world data.

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