Mary Noticed That Old Coins Are Smoother and More Worn $$\begin{array} { c c r l } r ^ { 2 } & 0.442 & n & 31 \\r & - 0.665 & k & 1 \\\text { or } & 0.050 & \text { Dep. Var. Weight (gm) }\end{array}$$

Essay

Mary noticed that old coins are smoother and more worn. She weighed 31 nickels and recorded their ages, and then performed a simple regression to estimate the model Weight = β₀ + β₁ Age, where weight is the weight of the coin in grams and Age is the age of the coin in years. Her results are shown below. Write a brief analysis of these results, using what you have learned in this chapter. Make a prediction of Weight when Age = 10 and also when Age = 20. What does this tell you? Is the intercept meaningful in this regression?
Regression Analysis
$$\begin{array} { c c r l } r ^ { 2 } & 0.442 & n & 31 \\r & - 0.665 & k & 1 \\\text { or } & 0.050 & \text { Dep. Var. Weight (gm) }\end{array}$$

ANOVA table
$\begin{array}{rcccrr}\hline \text { Source } & \text { SS } & \text { df } & M S & F & p \text {-value } \\\hline \text { Regression } & 0.0582 & 1 & 0.0582 & 22.99 & 4.48 \mathrm{E}-05 \\\text { Residual } & 0.0734 & 29 & 0.0025 & & \\\hline \text { Total } & 0.1316 & 30 & &\end{array}$


Regression output                                                 confidence interval
$\begin{array}{crrrrrr}\hline \text { variables } & \text { coefficients } & \text { std. emor } & f(d f=29) & \text { p-value } & 95 \% \text { lower } & 95 \% \text { upper } \\\hline \text { Intercept } & 5.0210 & 0.0137 & 367.740 & 9.33 \mathrm{E}-55 & 4.9931 & 5.0489 \\\text { Age (Yrs) } & -0.0040 & 0.0008 & -4.795 & 4.48 \mathrm{E}-05 & -0.0057 & -0.0023 \\\hline\end{array}$