Question

name:
unit 3 exam (a)
period: 1 date 11/5
directions: answer the following questions to the best of your ability. you are working silent and solo.
→ for multiple choice questions (#1 - #3), circle the correct answer(s).
→ for free response questions (#4 - #6), explain your reasoning by circling the correct answer from the underlined options, filling in the blank, and using the vocabulary in the word blank

1. which one of these graphs represents the residuals for a scatter plot that is fit well by a linear model?
2. twenty - one young men got a quote for the cost of a car insurance policy. the policy cost and ages of the men are represented by the scatter plot.

select the two the statements that are true about the data in ( y=-315.67x + 8986.5 )
( r=-0.951 )
a. every 19 - year - old in this group has a lower cost of car insurance than the 18 - year - olds.
b. car insurance policy cost tends to decrease as the age of a driver increases.
c. the value of the correlation coefficient is very close to - 1, so there is no association between age and car insurance policy cost.
d. the line of best fit indicates that, in general, the cost of a car insurance policy for a 21 - year - old should be, on average, about $315 less than the cost of a car insurance policy for a 20 - year - old.
e. the y - intercept from the line of best fit indicates that, if the linear trend holds, a car insurance policy would be $0 for a person who is about 8,987 years old.

Explanation:

Step1: Analyze option a

The scatter - plot does not imply that every 19 - year - old has a lower cost than every 18 - year - old. There could be overlap in the data points for different ages.

Step2: Analyze option b

The slope of the regression line \(y=-315.67x + 8986.5\) is negative (\(m=-315.67\)). In a linear regression model \(y = mx + b\), a negative slope means that as \(x\) (age) increases, \(y\) (car insurance cost) decreases.

Step3: Analyze option c

A correlation coefficient \(r=-0.951\) (close to - 1) indicates a strong negative association, not no association.

Step4: Analyze option d

The slope of the regression line \(m=-315.67\). This means that for each one - unit increase in \(x\) (age), \(y\) (car insurance cost) decreases by approximately \(315.67\). So, the cost for a 21 - year - old (\(x = 21\)) is about \(315.67\) less than the cost for a 20 - year - old (\(x = 20\)) on average.

Step5: Analyze option e

The \(y\) - intercept \(b = 8986.5\) in the equation \(y=-315.67x + 8986.5\) is the value of \(y\) when \(x = 0\), not when \(y = 0\). To find when \(y = 0\), we solve \(0=-315.67x+8986.5\), \(x=\frac{8986.5}{315.67}\approx28.5\)

Answer:

b. Car insurance policy cost tends to decrease as the age of a driver increases.
d. The line of best fit indicates that, in general, the cost of a car insurance policy for a 21 - year - old should be, on average, about \(\$315\) less than the cost of a car insurance policy for a 20 - year - old.