How tall a kid should be for their age
Parents often worry whether their child is tall enough. The data set provided by Mr. Kris Kringle can answer this dilemma by helping us to predict the height of a kid based on their age. No longer will parents find themselves wondering whether their child is able to keep up with other children, as they will see exactly how far from average their messed up offspring really is.
To analyze the data I used a program called R with simple linear regression using an alpha level of 0.05. The initial analysis of the data did not show any problems indicative of errors, and I believe it is reasonable to assume this data set is a good representation of all youth growing up on the North Pole.
A simple linear regression model predicting height based on age had a residual plot with no discernable patterns which suggests the model I have used is appropriate for this data set. You can see this in the plot below.
The results from the regression model showed a slope of 2.5774 which means that each age we expect the height of the child to increase by 2.5774 inches. Because the p-value was small (nearly zero) which is less than the alpha of 0.05 we can say with certainty that as a child ages their height increases. That relationship is shown in the plot below
The equation for predicting height is height = 27.92 + 2.58 *age.
I am 95% confident that the effect of age on height is between 2.18 and 3.03.
Mr. Kringle requested a predicted height value for a 10 year old boy. Using this equation I would predict 27.92 + 2.58*10 = 53.7 inches tall. This prediction will be accurate within 6.628 inches. That means the boy could be between 47.07 and 60.33 inches, or even (if he is rare) between 40.44 to 66.96 inches tall.
That means the boy could be between 47.07 and 60.33 inches with 68% confidence, or even (if he is rare) between 40.44 to 66.96 inches tall with 95% confidence.
I am 95% confident he will be between 40.44 and 66.96 inches tall, with an expected value of 53.7 inches.
I am 95% confident he will be between 40.47 and 66.92 inches tall, with an expected value of 53.7 inches.
The R2 is .51 indicating that just over half the variability in children’s heights can be attributed to their age.
Thus in conclusion, we see that children grow about 2 inches in height per year. This means if your child grows more than that they might be in a growth spurt, but if your child grows less than that consistently you may worry about a growth hormone disorder. Future studies should look into whether it matters as to the gender of the child, and look into the relationship between age and height for older children.