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A local SPCA surveyed 15 people and collected data based on the number of cats owned and the age of the owner.

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  1. 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 r2 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. 

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(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




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ima (2).gif

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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

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(Q 3] eruafiohj We => (‘7: 00629;: +0.2934 . #mhen X ripma—eh/fi 8181
. J vrzflwnb Mmfl 011% 6” a: : 5oymrJ y: 0.0519 X50 +0.23%
=3_4384 .. j: 0.062‘3X32 +...

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