Chapter 3.4, Problem 28AYU

(a)

To determine

To draw: a scatter diagram of the given data

Answer to Problem 28AYU

  

Explanation of Solution

Given:

  

Calculation:

Draw a scatter diagram of the data treating speed as the independent variable and find the type of relation appears to exist between speed and miles per gallon

From the scatter plot of the data it is seen that there is quadratic relation exists between speed

and miles per gallon.

Conclusion:

Thus, the scatter diagram is drawn.

(b)

To determine

To find: the quadratic function of best fit

Answer to Problem 28AYU

The relation between speed and miles per gallon is given below;

  $M=-\frac{1}{60}{s}^2+\frac{563}{300}s-\frac{49}{2}$

Explanation of Solution

Calculation:

The linear model that describes the relation between speed and miles per gallon is given below;

  $M=-\frac{1}{60}{s}^2+\frac{563}{300}s-\frac{49}{2}$

Conclusion:

The relation between speed and miles per gallon is given below;

  $M=-\frac{1}{60}{s}^2+\frac{563}{300}s-\frac{49}{2}$

(c)

To determine

miles per gallon for the Camry that is travelling 63 miles per hours

Answer to Problem 28AYU

Hence, miles per gallon for the Camry that is travelling 63 miles per hours is $27.58$

Explanation of Solution

Calculation:

To predict miles per gallon for the Camry that is travelling 63 miles per hours, substitute $s=63$ in the quadratic model that describes the relation between speed and miles per gallon.

  $M=-\frac{1}{60}{(63)}^2+\frac{563}{300}(63)-\frac{49}{2}=-66.15+118.23-24.5=27.58$

Hence, miles per gallon for the Camry that is travelling 63 miles per hours is $27.58$

Conclusion:

Hence, miles per gallon for the Camry that is travelling 63 miles per hours is $27.58$