The data in Table 7 shows that the percentage of male...

The data in Table 7 shows that the percentage of male cigarette smokers in the U.S. declined from $27.6 \%$ in 1997 to $23.9 \%$ in $2006 .$ (A) Applying linear regression to the data for males in Table 7 produces the model $$ m=-0.42 t+27.23 $$ where $m$ is percentage of male smokers and $t$ is time in years since $1997 .$ Draw a scatter plot of the male smoker data and a graph of the regression model for $0 \leq t \leq 30$ (B) Estimate the first year in which the percentage of male smokers is less than $15 \%$

The data in Table 7 shows that the percentage of male cigarette smokers in the U.S. declined from $27.6 \%$ in 1997 to $23.9 \%$ in $2006 .$
(A) Applying linear regression to the data for males in Table 7 produces the model
$$
m=-0.42 t+27.23
$$
where $m$ is percentage of male smokers and $t$ is time in years since $1997 .$ Draw a scatter plot of the male smoker data and a graph of the regression model for $0 \leq t \leq 30$
(B) Estimate the first year in which the percentage of male smokers is less than $15 \%$

Key Concepts

Scatter Plot

A scatter plot is a type of data visualization that displays individual data points on a two-dimensional graph, with one axis representing the independent variable and the other representing the dependent variable. This visual tool helps in identifying trends, patterns, correlations, and potential outliers in the data, which is crucial before applying any regression analysis.

Solving Linear Equations/Inequalities

Solving linear equations or inequalities involves manipulating a linear expression to find the value(s) of the variable that satisfies the given condition. In the context of a regression model, this technique is used to determine when a particular target level occurs, such as the point at which a percentage falls below a specified threshold.

Extrapolation

Extrapolation is the process of estimating values outside the range of observed data by extending the established trend from the regression model. While it can provide useful predictions, it should be done with caution since the model's reliability is best within the range of the original data.

Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation. It helps in understanding how the dependent variable changes as the independent variable varies, with the slope indicating the rate of change and the y-intercept representing the starting value when the independent variable is zero.

Predictive Modeling

Predictive modeling involves using a statistical model, such as a linear regression model, to forecast future values of a variable based on past data. In this context, it is used to estimate when a particular threshold will be reached, giving insights into future trends based on historical patterns.

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