Exercise 3 Page 25

Practice makes perfect

a The data does not follow an exact linear relationship. However, we can see a clear upward trend, which means that we can draw a line of best fit.

The drawn line of fit intercepts the y-axis at 65 and also passes through (5,80). We can calculate the slope of the function using the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,65) & ( 5,80)

m=80- 65/5- 0

SubTerms

Subtract terms

m=15/5

CalcQuot

Calculate quotient

m=3

We can put m=3 together with the y-intercept b=65 to write a function rule in slope-intercept form. y=3x+65 Now that we have the function rule, we can estimate the height of a female with a humerus 40 cm long.

y=3x+65

Substitute

x= 40

y=3( 40)+65

Multiply

y=120+65

y=185

Therefore, according to our line of fit, a female whose humerus is 40 cm long should be 185 cm tall.

b Before we perform a linear regression, we first have to enter the values into lists. Push STAT, choose Edit, and then enter the values in the first two columns.

To do a linear regression, we push STAT, scroll right to CALC, and then choose the fourth option in the list, LinReg.

The line of best fit has the following function rule. y=3.1x+63.5 We can estimate the height of a female with a humerus 40 cm long by substituting 40 for x.

y=3.1x+63.5

Substitute

x= 40

y=3.1( 40)+63.5

Multiply

y=124+63.5

AddTerms

Add terms

y=187.5

Thus, our estimation of 185 cm was quite accurate. The difference is equal to only 2.5 cm.