Interpreting Correlation

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Show your work for each problem.

1.
On a mountain hike, the correlation between altitude and air temperature is $r = -0.92$ . How do you describe it?
1. a)Weak negative
2. b)Strong positive
3. c)Strong negative
4. d)No linear correlation
2.
Which value of $r$ shows the weakest linear relationship?
1. a) $0.47$
2. b) $-0.08$
3. c) $0.56$
4. d) $-0.85$
3.
The correlation between the number of hours a phone is used per day and its remaining battery in the evening is $r = -0.54$ . What is $|r|$ , the number that gives the strength?
4.
Four studies report $r = 0.35$ , $r = -0.81$ , $r = 0.57$ and $r = -0.18$ . Type the value of $r$ that shows the strongest linear relationship.
5.
For 30 students, the correlation between study time per week and the grade on a final exam is $r = 0.78$ . Describe the correlation step by step.
6.
In a survey of 80 families, the correlation between the distance from home to school (km) and the number of days per week the children walk to school is $r = -0.47$ . Find the strength step by step.
7.
For 50 teenagers, the correlation between hours of sleep and the score on a reaction test (higher is better) is $r = 0.52$ . Which sentence is the best interpretation?
1. a)52% of the teenagers who sleep more score higher.
2. b)There is a moderate negative correlation: teenagers who sleep more tend to score lower.
3. c)There is a moderate positive linear correlation: teenagers who sleep more tend to score higher.
4. d)There is a strong positive correlation, so more sleep causes higher scores.
8.
A scatter plot shows a clear U shape, but the calculator gives $r \approx 0.01$ . Which conclusion is correct?
1. a)The value of $r$ must have been calculated wrongly
2. b)There is almost no linear relationship, but a strong curved one
3. c)There is no relationship at all between the variables
4. d)There is a strong positive linear correlation
9.
For 25 adults, the correlation between height in cm and weight in kg is $r = 0.71$ . A researcher changes the heights to meters and the weights to grams. What is $r$ now?
10.
Using the rule of thumb ( $|r| \ge 0.7$ is strong), how many of these values show a strong correlation? $0.72$ , $-0.91$ , $0.59$ , $-0.45$ , $0.70$ , $0.38$
11.
Study A finds $r = -0.74$ between the price of a concert ticket and the number of tickets sold. Study B finds $r = 0.56$ between advertising spending and tickets sold. Which correlation is stronger?
12.
For 40 taxi rides, the correlation between distance in km and fare in dollars is $r = 0.83$ . The company then writes every fare in cents and every distance in miles.
13.
For 60 students, the correlation between hours of video games per week and the grade average (higher is better) is $r = -0.58$ . Build an interpretation sentence.
14.
Eight points form a round cloud with no pattern, $r \approx 0.05$ . One new point is added far away in the top right corner of the scatter plot. What happens to $r$ ?
1. a)It becomes strongly negative
2. b)It becomes strongly positive
3. c)It stays about $0.05$
4. d)It becomes exactly $0$
15.
The points $(-2, 4)$ , $(-1, 1)$ , $(0, 0)$ , $(1, 1)$ , $(2, 4)$ lie exactly on the curve $y = x^2$ . Here $\bar{x} = 0$ and $\bar{y} = 2$ , and the numerator of $r$ is $\sum (x - \bar{x})(y - \bar{y})$ . What is $r$ ?
16.
A ball is thrown up. Its height (m) after $0, 1, 2, 3, 4$ seconds is $0, 3, 4, 3, 0$ . Find $r$ between time and height and interpret it.
17.
Plot E: six students give $r \approx 0.999$ between practice hours and quiz score. With the seventh student, the point $(7, 40)$ , $r \approx 0.14$ . Analyze the outlier.
18.
An ice cream shop finds $r = 0.9$ between the daily temperature in °C and the number of ice creams sold. The owner converts the temperatures to °F with $F = 1.8C + 32$ and then also swaps the axes.