Question

1 select all the values for r that indicate a positive slope for the line of best fit.
a 1 b -1
c 0.5 d -0.5
e 0 f 0.8
g -0.8
2 the correlation coefficient, r, is given for several different data sets. which value for r indicates the strongest correlation?
a 0.01 b -0.34
c -0.82 d -0.95
3 which of the values is the best estimate of the correlation coefficient for the line of best fit for the data represented by the scatter plot?
a -0.9 b 0.4
c -0.4 d 0.9

Explanation:

Question 1

Step1: Recall the property of \(r\) and slope

The sign of the correlation coefficient \(r\) is the same as the sign of the slope of the line of best fit. Positive \(r\) means positive - slope.

Step2: Check each option

• Option A: \(r = 1>0\), so it has a positive slope.
• Option B: \(r=-1 < 0\), it has a negative slope.
• Option C: \(r = 0.5>0\), so it has a positive slope.
• Option D: \(r=-0.5 < 0\), it has a negative slope.
• Option E: \(r = 0\), the line of best fit is horizontal (slope \(m = 0\)).
• Option F: \(r = 0.8>0\), so it has a positive slope.
• Option G: \(r=-0.8 < 0\), it has a negative slope.

Step1: Recall the formula for the strength of correlation

The strength of the correlation is determined by the magnitude of \(r\), \(|r|\in[0,1]\). The closer \(|r|\) is to \(1\), the stronger the correlation.

Step2: Calculate the magnitude of each \(r\)

• For \(r = 0.01\), \(|r|=0.01\)
• For \(r=-0.34\), \(|r| = 0.34\)
• For \(r=-0.82\), \(|r|=0.82\)
• For \(r=-0.95\), \(|r|=0.95\)

Since \(0.95>0.82>0.34>0.01\)

Step1: Determine the sign of \(r\)

The scatter - plot shows an upward trend. So \(r>0\) (positive correlation).

Step2: Determine the magnitude of \(r\)

The points are relatively close to the line of best fit. A value of \(r = 0.9\) (closer to \(1\)) indicates a strong positive correlation, while \(r = 0.4\) indicates a weak positive correlation.

Answer:

A. 1, C. 0.5, F. 0.8

Question 2