Question

review day 1
name nolave mugaga hr 3

1. correlation is a measure of (circle one)

a. center
b. spread
c. association

1. correlation cannot have a value of. (circle one)

a. 0.3
b -0.5
c 1.1
d 0.0
e. 0.98

1. the linear regression for the amount of time (minutes, y) it takes to shovel your driveway is based on how much it snowed (inches x) is y = 12x + 10. if you have 14 inches of snow, how many minutes would you expect it to take to shovel your driveway? (circle one)

a. 33 b 178 c. 1224 d. 308

1. the following scatter - plot displays data for years of experience and income (in thousands of dollars)

a. describe the relationship in the scatter plot
there is a strong positive linear
b. determine which variable is the explanatory variable and which is the response variable.
c. which of the following is the most appropriate estimate of the correlation coefficient r?
0.39 -0.65 1.0 0.0 0.89
d. how would adding the point (35, 20) affect the value of the correlation coefficient and the strength of the relationship?

Explanation:

Step1: Recall correlation definition

Correlation measures the linear - association between two variables. So for question 1, the answer is 'association'.

Step2: Recall correlation coefficient range

The correlation coefficient $r$ ranges from - 1 to 1. So a value of 11 is not possible for a correlation coefficient for question 2.

Step3: Substitute value into linear regression equation

For question 3, given $y = 12x+10$ and $x = 14$, we substitute $x$: $y=12\times14 + 10=168 + 10=178$.

Step4: Analyze scatter - plot for question 4a

The scatter - plot shows a strong positive linear relationship as the points follow an upward - sloping linear pattern.

Step5: Identify explanatory and response variables for question 4b

The number of years of experience is likely to explain the income. So years of experience is the explanatory variable and income is the response variable.

Step6: Estimate correlation coefficient for question 4c

Since it is a strong positive linear relationship, an estimate of $r = 0.89$ is appropriate as values close to 1 indicate strong positive linear correlations.

Step7: Analyze the effect of an out - lying point for question 4d

The point $(35,20)$ is an outlier. Adding it would decrease the value of the correlation coefficient and weaken the strength of the relationship as it does not follow the general pattern of the other points.

Answer:

1. c. Association
2. c. 11
3. b. 178

4.
a. There is a strong positive linear relationship.
b. Explanatory variable: Years of Experience; Response variable: Income
c. 0.89
d. It would decrease the value of the correlation coefficient and weaken the strength of the relationship.