Answer to Question #267948 in Statistics and Probability for alisha

Question

A study is conducted to determine the relationship between a driver’s age and the number of accidents he or she has over a 1-year period. The data are shown here. a. Draw the scatter plot. (2 marks) b. Compute the value of the correlation coefficient. (2 marks) c. Test the significance of the correlation coefficient at  = 0.01. (5 marks) d. Determine the regression line equation. (2 marks) e. Predict the number of accidents of a driver who is 28.

Answer 1

Drivers Age x - 16, 24, 18, 17, 23, 27, 32

No. of accidents y - 3, 2, 5, 2, 0, 1, 1

a.

b.

correlation coefficient:

$r=\frac{\sum(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum(x_i-\overline{x})^2(y_i-\overline{y})^2}}$

$\overline{x}=22.4,\overline{y}=2$

$r=-0.61$

c.

Null Hypothesis: H₀: r=0

Alternate Hypothesis: H_a: r≠0

test statistic:

$t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\frac{-0.61\sqrt{5}}{\sqrt{1-0.61^2}}=-1.721$

$df=n-2=5$

critical value:

$t_{crit}=4.032$

Since $|t|<t_{crit}$ we accept Null Hypothesis. Correlation coefficient IS NOT significantly different from zero. There IS NOT a significant linear relationship(correlation) between x and y.

d.

equation of regression line:

$y=ax+b$

$a=\frac{\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}=-0.1701$

$b=\frac{\sum y\sum x^2-\sum x\sum xy}{n\sum x^2-(\sum x)^2}=5.816$

$y=5.816-0.1701x$

e.

number of accidents of a driver who is 28:

$y(28)=5.816-0.1701\cdot28=1.05\approx 1$ accident