Question

2 Analyze the scatter plot relating a male chihuahua's weight with its age.

Draw the line of best fit for the set
of data vaules. Then determine the
equation for the line of best fit.
Interpret the meaning of the slope and
y-intercept for your equation.
Weight (pounds)
Use your line of best fit to predict the weight of a 9-week-old male chihuahua.

Answer 1

a) y = 1.5x + 9

b) Slope: Weight increases by 1.5 pounds for each additional week of age.

y-intercept: Estimated birth weight is 9 pounds.

c) 22.5 pounds

Explanation:

Part (a)

The given scatter plot relates a male chihuahua's weight with its age.

The independent variable (x) is the age, and the dependent variable (y) is the weight.

The line of best fit of a scatter plot is a straight line that represents the general trend or pattern. It should pass as close as possible to the majority of the data points.

The line of best fit for the given scatter plot passes through the first point (0, 9) and the fifth point (24, 45), with two points above and two points below the line, thereby minimizing the overall distance between the line and the points. (See attachment).

The equation of the line of best fit is:

`y = 1.5x + 9`

`\hrulefill`

Part (b)

The slope indicates that, on average, the chihuahua's weight increases by 1.5 pounds for each additional week of age.

The y-intercept suggests that the estimated weight of the male chihuahua at birth (age zero weeks) is 9 pounds.

`\hrulefill`

Part (c)

To predict the weight of a 9-week-old male chihuahua, substitute x = 9 into the equation of the line of best fit:

`y=1.5(9)+9`

`y=13.5+9`

`y=22.5`

Therefore, the predicted weight of a 9-week-old chihuahua is approximately 22.5 pounds.