Answer to Question #238338 in Statistics and Probability for Ndilloh

Question

Consider the “height-for-age” data below:
Table 3: Height for age data
Age in Years
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Height in cm
102
107
112
116
121
126
130
136
143
149
154
158
161
162
163
a) Make a scatter plot of the data.

b) Find the least square regression line and add it to the scatter plot in Question 6 a).

c) Find the coefficient of determination and state what it tell us about the relationship between Age and
Height

d) Going by the relationship between Age and Height that you have established:
i) What would the expected value of Height be if Age is 90 years?

ii) Will the linear models be the best model for "height-for-age data"? JUSTIFY YOUR ANSWER!

Answer 1

SOLUTION

a) Make a scatter plot of the data.

Solution:

I used Microsoft excel software to make a scatter plot of the data

b) Find the least square regression line and add it to the scatter plot in Question 6 a).

Solution:

I used excel to get the trendline and the least square regression (R²)

c) Find the coefficient of determination and state what it tell us about the relationship between Age and Height.

Solution:

I used the excel function, RSQ to get the coefficient of determination

The function is =RSQ(A2:A16,B2:B16)

From the graph presentation and the value of R², the age in years is positively related to the height in cm

d) Going by the relationship between Age and Height that you have established:

i) What would the expected value of Height be if Age is 90 years?

ii) Will the linear models be the best model for "height-for-age data"?

Solution

i) Using the least square regression line, $y=1.7429x+79.086$

Let $x=90 years$, Then let replace 90 years to the function to get the expected value of height.

$y=(1.7429*90)+79.086$

$y=235.947$

$Answer=235.947$

ii) The linear models of age 90 years and height of 235.947 will not fit to be the best model for "height-for-age data" because it fit less the best fit line and has decimal values.