Exercise 36 Page 210

a The slope

m

tells us the steepness of the line. The

y -

b

shows where the line cuts the

y -

axis. Examining the line of best fit, we can identify these values.

y = 0.253 + 0.735 x

A slope of

0.735

means that for every extra ounce of meat we buy, the price increases on average by

$ 0.735 .

The

y -

intercept of

0.253

tells us that if we buy

0

ounces of meat, the cost is

$ 0.253 .

However, this does not make sense, since then you would have to pay even if you did not buy anything.

b The residual is the actual value minus the predicted value.

Residual = Actual value - Predicted value

From the exercise, we know that the actual value when buying

3

oz. of meat is

$ 3.20 .

To calculate the predicted value, we have to substitute

x = 3

into the line of best fit.

y = 0.253 + 0.735 x

$x = 3$

y = 0.253 + 0.735 (3)

y = 0.253 + 2.205

Add terms

y = 2.458

Having calculated the predicted value, we can find the residual.

Residual = 3.2 - 2.458 = 0.742

Since the residual is positive, the model understates the cost at this level.

c One pound equals

16

ounces. If the price is reasonable, the model from Part A should give a price that is roughly around

$ 14.70

when substituting

16

for

x .

y = 0.253 + 0.735 x

$x = 16$

y = 0.253 + 0.735 (16)

y = 0.253 + 11.76

Add terms

y = 12.013

The price should be around

$ 12

according to the model. Therefore, the price in the home town is a bit too high to be reasonable.

4.1.1 Line of Best Fit p.196-197

4.1.2 Residuals p.201-202

4.1.3 Upper and Lower Bounds p.205-206

4.1.4 Least Squares Regression Line p.210-213