Chapter 3, Problem 11PT

(a)

To determine

To make: a scatter plot of the givne data.

Answer to Problem 11PT

  

Explanation of Solution

Given:

Age	36	48	51	54	57	60
height	86	90	91	93	94	95

Calculation:

The scatter plot for the given data is as follows

  

From the scatter plot, we can see that all points are showing a linear trend in upward direction. Hence, we can say that there exists a positive correlation between Age and Height. In other words, we can say that Age and Height are positively correlated.

Conclusion:

Hence,scatterplot is drawn.

(b)

To determine

To find: The equation of the least − squares regression line of height on age.

Answer to Problem 11PT

The least-square regression line is $\text{Height = 71}\text{.95+0}\text{.0383 Age}$

Explanation of Solution

Calculation:

Here “age” is the explanatory variable and “height” is the response variable.

Using MINITAB, the output of the least − square regression line is obtained as follows.

Regression Analysis: Height versus Age

  

From the above output, the least-square regression line is given by

  $\text{Height = 71}\text{.95+0}\text{.0383 Age}$

Conclusion:

Hence, the least-square regression line is $\text{Height = 71}\text{.95+0}\text{.0383 Age}$

(c)

To determine

To predict: S’s height at age 40 years

Answer to Problem 11PT

S’s height will be 100.7677 inches.

Explanation of Solution

Calculation:

From part (b), the regression line between Age and Height is obtained as

Height = 71.95+0.0383 Age

Using the above regression line, we can predict Sarah’s height at age 40 years (480 months)

That is, the predicted Sarah’s height at age 40 years (480 months) will be,

  

Conclusion:

Hence, the predicted Sarah’s height at age 40 years (480 months) will be 100.7677 inches.

(d)

To determine

To explain: why the prediction is impossibly large.

Answer to Problem 11PT

Predicting Sarah’s height at age 40 years (480 months) is an extrapolation of the relationship beyond what the data show.

Explanation of Solution

Age of 40 years (480 months) is far outside the set of X- values for our data. We cannot say whether the relationship remains linear at such extreme values. Predicting Sarah’s height at age 40 years (480 months) is an extrapolation of the relationship beyond what the data show. Hence, we can say that the predicted height is not accurate