Instructions for Exercises 12.18-12.20: (a) Use Excel to...

Instructions for Exercises 12.18-12.20: (a) Use Excel to make a scatter plot of the data. (b) Select the data points, right-click, select Add Trendline, select the Options tab, and choose Display equation on chart and Display R-squared value on chart. (c) Interpret the fitted slope. (d) Is the intercept meaningful? Explain. (e) Interpret the $R^2$. $$ \begin{array}{cc} \hline & \begin{array}{l} \text { Moviegoer Snack } \\ \text { Spending }(\boldsymbol{n}=10) \\ \text { Movies } \end{array} \\ \hline \text { Age }(\boldsymbol{X}) & \text { Spent }(\boldsymbol{Y}) \\ \hline 30 & 2.85 \\ 50 & 6.50 \\ 34 & 1.50 \\ 12 & 6.35 \\ 37 & 6.20 \\ 33 & 6.75 \\ 36 & 3.60 \\ 26 & 6.10 \\ 18 & 8.35 \\ 46 & 4.35 \\ \hline \end{array} $$

Instructions for Exercises 12.18-12.20: (a) Use Excel to make a scatter plot of the data. (b) Select the data points, right-click, select Add Trendline, select the Options tab, and choose Display equation on chart and Display R-squared value on chart. (c) Interpret the fitted slope. (d) Is the intercept meaningful? Explain. (e) Interpret the $R^2$.
$$
\begin{array}{cc}
\hline & \begin{array}{l}
\text { Moviegoer Snack } \\
\text { Spending }(\boldsymbol{n}=10) \\
\text { Movies }
\end{array} \\
\hline \text { Age }(\boldsymbol{X}) & \text { Spent }(\boldsymbol{Y}) \\
\hline 30 & 2.85 \\
50 & 6.50 \\
34 & 1.50 \\
12 & 6.35 \\
37 & 6.20 \\
33 & 6.75 \\
36 & 3.60 \\
26 & 6.10 \\
18 & 8.35 \\
46 & 4.35 \\
\hline
\end{array}
$$

Key Concepts

Coefficient of Determination (R-squared)

The coefficient of determination, denoted as R-squared, measures the proportion of variance in the dependent variable that is predictable from the independent variable(s). It ranges between 0 and 1, where values closer to 1 indicate a better fit of the model to the data. R-squared helps in evaluating the explanatory power of the regression model.

Intercept in Regression

The intercept in a regression model is the estimated value of the dependent variable when the independent variable is zero. It serves as a starting point for the regression line on the y-axis. However, its practical significance depends on whether a value of zero is meaningful or relevant for the context of the data being analyzed.

Slope in Regression

The slope in a regression equation quantifies the change in the dependent variable for each one-unit increase in the independent variable. It represents the strength and direction of the relationship between the variables, where a positive slope indicates an upward trend and a negative slope indicates a downward trend.

Linear Regression Analysis

Linear regression analysis is a statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables. By fitting a linear equation to the observed data, it provides estimates of the relationship in terms of a slope and an intercept, and allows for predictions of the dependent variable based on new values of the independent variable.

Scatter Plot

A scatter plot is a graphical representation of data points on a two-dimensional plane where each point represents the values of two variables. It is used to visually assess the relationship, trends, or patterns between the independent and dependent variables, helping to identify potential correlations or outliers.

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