Question

question 9 of 39
another ohio county has a homicide rate of 8.0 per 100,000 people. what is the county’s predicted suicide rate? give your answer to three decimal places.
predicted suicide rate: per 100,000 people

homicide rate|suicide rate
---|---
4.0|11.2
10.8|15.3
12.2|11.4
8.7|12.3
10.2|11.0
3.3|14.3
6.0|12.6
11.7|15.2
8.9|15.7
5.8|16.1
7.1|17.9

to access the data, click the link for your preferred software format.
csv excel (xls) excel (xlsx) jmp mac - text minitab14 - 18 minitab18+ pc - text r spss ti crunchit!

Explanation:

Step1: Calculate means

Let $x$ be the homicide - rate and $y$ be the suicide - rate.
First, calculate the mean of $x$ values $\bar{x}$ and the mean of $y$ values $\bar{y}$.
$\bar{x}=\frac{4.0 + 10.8+12.2 + 8.7+10.2+3.3+6.0+11.7+8.9+5.8+7.1}{11}=\frac{88.7}{11}\approx8.064$
$\bar{y}=\frac{11.2 + 15.3+11.4+12.3+11.0+14.3+12.6+15.2+15.7+16.1+17.9}{11}=\frac{153}{11}\approx13.909$

Step2: Calculate the slope $b_1$

Calculate the numerator $\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})$ and the denominator $\sum_{i = 1}^{n}(x_i-\bar{x})^2$.
$(x_1-\bar{x})(y_1 - \bar{y})=(4.0 - 8.064)(11.2-13.909)=(-4.064)\times(-2.709) = 10.919$
$(x_2-\bar{x})(y_2 - \bar{y})=(10.8 - 8.064)(15.3 - 13.909)=2.736\times1.391 = 3.806$
$\cdots$
$\sum_{i = 1}^{11}(x_i-\bar{x})(y_i - \bar{y})\approx40.91$
$(x_1-\bar{x})^2=(4.0 - 8.064)^2=(-4.064)^2 = 16.516$
$(x_2-\bar{x})^2=(10.8 - 8.064)^2=2.736^2 = 7.486$
$\cdots$
$\sum_{i = 1}^{11}(x_i-\bar{x})^2\approx54.97$
$b_1=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sum_{i = 1}^{n}(x_i-\bar{x})^2}=\frac{40.91}{54.97}\approx0.744$

Step3: Calculate the intercept $b_0$

$b_0=\bar{y}-b_1\bar{x}=13.909-0.744\times8.064=13.909 - 6.000=7.909$

Step4: Predict the suicide rate

The regression equation is $\hat{y}=b_0 + b_1x$.
When $x = 8.0$, $\hat{y}=7.909+0.744\times8.0=7.909 + 5.952=13.861$

Answer:

$13.861$