Question

1. identify the correlation you would expect to see between household income and the number of electronic devices a family owns.

Explanation:

Question 12:

Step1: Analyze the scatter plot

The scatter plot shows elevation (in meters) on the y - axis and mean annual temperature (in °C) on the x - axis for locations in Nevada. As elevation increases, the mean annual temperature generally decreases. The points show a somewhat linear trend, but there is some scatter.

Step2: Describe the correlation

Since as one variable (elevation) increases, the other (mean annual temperature) decreases, the correlation is negative. The points are somewhat clustered around a line, so it is a moderate to strong negative correlation.

Step3: Estimate the correlation coefficient

A perfect negative correlation is - 1, and a perfect positive is 1. Given the scatter, an estimate could be around - 0.7 to - 0.8. (The exact value would require calculation, but visually, it's a relatively strong negative linear relationship.)

Step1: Recall the rule for correlation strength

The strength of a correlation is determined by the absolute value of the correlation coefficient. The closer the absolute value is to 1, the stronger the correlation. If the absolute value is close to 0, the correlation is weak.

Step2: Order the absolute values

First, find the absolute values of each coefficient: \(|0.93| = 0.93\), \(|- 0.23|=0.23\), \(|0.52| = 0.52\), \(|-0.87| = 0.87\).
Now, order the absolute values from smallest to largest: \(0.23<0.52<0.87<0.93\).
Since the sign indicates the direction (positive or negative) and the absolute value indicates the strength, the order from weakest to strongest correlation (based on strength, ignoring direction for ordering strength) is: \(- 0.23\), \(0.52\), \(- 0.87\), \(0.93\).

Step1: Recall the interpretation of correlation coefficient

A correlation coefficient \(r\) with \(|r|\) close to 0 indicates a weak correlation, close to 1 (or - 1) indicates a strong correlation. The sign indicates the direction (positive for positive association, negative for negative association).

Step2: Interpret \(r=-0.23\)

The correlation coefficient is - 0.23. The negative sign indicates a negative association (as one variable increases, the other tends to decrease). The absolute value of 0.23 is relatively small (close to 0), so it indicates a weak negative linear correlation between the two variables.

Answer:

The correlation between elevation and mean annual temperature in Nevada is a moderate to strong negative linear correlation. An estimated correlation coefficient is around - 0.75 (answers between - 0.7 and - 0.8 are reasonable).

Question 13: