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a) Describe the relationship between height and weight.

Answer:There appears to be a linear relationship between the height and weight. As height increases so is weight.

b) Write the equation for the regression line. Interpret the slope and interpret in the context.

Answer: \[\widehat{weight}=-105.0113 + 1.0176\text{ height} \] Slope:For every 1cm increase in height the average weight increases by 1.0176 kgs.

Intercept: Individuals who are 0 cms tall are expected to weight -105.0113 kgs. The negative slope is of no significance but the slope is necessary to adjust the level of the line.

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

Answer: \[\text{H_0 : The true slope is 0 }\] \[\text{H_A : The true slope is different from 0} \] As the p-value for the slope significance test is close to 0 we reject the null and conclude that the height and weight are positively correlated.

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

Answer: \(R^2=0.72^2=0.52\)

Approximately 52% of the variability in weight can be explained by the height of individuals.

0.72^2
## [1] 0.5184