(a) Describe the relationship between height and weight.

• Linear
• Positive
• Moderate

(b) Write the equation of the regression line. Interpret the slope and intercept in context.

\(\widehat{weight} = -105.0113 + 1.0176 * height\)

• Slope: For each additional cm in height, the regression line predicts the average weight to increase by 1.0176 kg
• Intercept: For height of 0 cm, the average weight is -105.0113

(c) Do the data provide strong evidence that an increase in height is associated with an increase in weight? State the null and alternative hypotheses, report the p-value, and state your conclusion.

\(H_0: \beta_1 = 0\) The true slope coefficient of height is 0.

\(H_A: \beta_1 > 0\) The true slope coefficient of height is greater than 0.

The \(p-value\) in the summary table is 0 (or very close to 0). This is for a two-sided test. In our case, a one-sided test, it's even lower. Therefore we reject the null hypothesis. The data provide strong evidence that an increase in height is associates with an increase in weight.

(d) The correlation coefficient for height and weight is 0.72. Calculate \(R^2\) and interpret it in context.

R <- 0.72
R2 <- R^2
R2

## [1] 0.5184

About \(R^2 = 0.5184\) or 51.84% of the variation in weight can be explained by the height.