- A local SPCA surveyed 15 people and collected data based on the number of cats owned and the age of the owner. The following scatterplot was created and a linear regression line was found

The regression line is *y* = 0.0629x + 0.2934, where *x* = the age of the cat owner in years and *y* = the number of cats owned. The value of *r*^{2} is 0.8462.

**(a)** Use the regression line to estimate the number of cats that someone who is 50 years old would own (round to the nearest whole number). Show some work.

**(b)** Use the regression line to predict the number of cats one would own when they are 92 years old. Show some work.

**(c)** What is the **slope** of the regression line and what are the units of measurement? In a sentence, interpret what the slope is telling us, in the context of this real-world application.

**(d)** What is the **value of the correlation coefficient, r**? Also,

**interpret its value**: Looking at the graph and the size of

*r*, do you judge the

**strength of the linear relationship**to be very strong, moderately strong, somewhat weak, or very weak?

**2 **Consider the graph of the piecewise function *y* = *f *(*x*) pictured below.

(a) State the value of *f *(5).

(b) State the *x*-intercept(s), if any.

(c) State the *y*-intercept(s), if any.

(d) State the domain of the piecewise function.

(e) State the range of the piecewise function.

(f) State **one** interval on which the function is increasing. That is, for what *x*-values is the function

increasing?

(g) State **one** interval on which the function is decreasing. That is, for what *x*-values is the function

decreasing?

3.What graph represents f(x) = - (x-2)^{2} + 1

#### Top Answer

1.a) 3 cats 1.b) 6 cats 1.c) 0.0629 cats/year 1.d) r = 0.92... View the full answer