Backpack weight backpack, in pounds, and the child's age, was recorded for a sample of Irish secondary school children. A simple linear regression, Yi = 0 + 1Xi + i , is fitted to the sample data, in order to explain the variability in backpack giving the following output: fit <- lm(backpack ~ age) summary(fit) Call: lm(formula = backpack ~ age) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -19.56 1.252 -15.616 0.000 age 1.78 0.081 22.134 0.000 Residual standard error: 1.076 on 48 degrees of freedom Multiple R-squared: 0.911,Adjusted R-squared: 0.909

Which one of the following statements is TRUE?

(a) Using this model, the backpack weight for an individual child that is aged 14 is estimated to be 8.2 pounds.

(b) The coefficient of the variable age, indicates the age increases by 1.78 on average for each 1 pound increase in the weight of the backpack.

(c) The estimated constant, -19.56, implies the backpack weight decreases by 19.56 pounds on average for each 1 year increase in age.

(d) s = 1.076 is an estimate of . The larger the value of s, the better the fit of the model to the data.

(e) Testing 1 = 0 versus 1 , 0, gives test statistic -15.616, which has p-value 0.000 and indicates age is not a good indicator of backpack weight in the population.

(f) Testing 1 = 0 versus 1 , 0, gives test statistic 22.134, which has p-value 0.000 and indicates age is a good indicator of backpack weight in the population