Suppose that George wants to determine if the number of insects in a given area is related to the number of flowers in that area. He creates three 1 m2 quadrats in his backyard and y Data point 1 X1 = 5 Yi = 17 counts the number of flowers (x) and number of insects (y) Data point 2 x2 = 9 y2 = 1 in each quadrat. His data are shown in the table. Data point 3 X3 = 10 Уз 3D 15 Calculate the Pearson product-moment correlation x = 8.00 Mean y = 11.00 coefficient, r, using the formula Standard deviation sd= 2.646 sd,= 8.718 Zxi r = п — 1 where z is the z-score for each value, x; represents the x-value for each data point, y; represents the y-value for each data point, and n represents the sample size. Complete the following five steps to calculate r, and give each of your answers precise to two decimal places. Step 1. Calculate the z-score for each x-value. X1 – x Zx1 = x2 - x Хз — х sdx Zx2 = Zx3 = sd. sd.

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Calculate Corellation coefeiccient step 5

Step 2. Calculate the z-score for each y-value.
Yi - ỹ
Zyl
sd,
y1
y
Уз — у
Zy3
sdy
y2 - y
Zy2
sdy
y
Step 3. For each data point, calculate the product of the pair of z-scores.
Zx1• Zyl
Zx2•Zy2 =
Zx3 · Zy3
Step 4. Sum the products of each pair of z-scores.
E(zxi • Zyi) =
II
Transcribed Image Text:Step 2. Calculate the z-score for each y-value. Yi - ỹ Zyl sd, y1 y Уз — у Zy3 sdy y2 - y Zy2 sdy y Step 3. For each data point, calculate the product of the pair of z-scores. Zx1• Zyl Zx2•Zy2 = Zx3 · Zy3 Step 4. Sum the products of each pair of z-scores. E(zxi • Zyi) = II
Suppose that George wants to determine if the number of
insects in a given area is related to the number of flowers in
that area. He creates three 1 m2 quadrats in his backyard and
Data point 1
X1 = 5
Yi = 17
counts the number of flowers (x) and number of insects (y)
Data point 2
X2
9.
Y2 = 1
in each quadrat. His data are shown in the table.
Data point 3
X3 = 10
Уз
= 15
Calculate the Pearson product-moment correlation
Mean
x = 8.00
y = 11.00
coefficient, r, using the formula
Standard deviation
sdx= 2.646
sdy= 8.718
E Zxi · Zyi
r =
п — 1
where z is the z-score for each value, x; represents the x-value for each data point, y; represents the y-value for each data
point, and n represents the sample size.
Complete the following five steps to calculate r, and give each of your answers precise to two decimal places.
Step 1. Calculate the z-score for each x-value.
X1
Zx1 =
X2
Zx2 =
X3 – x
sd.
sdx
sd.
Zx3 =
Transcribed Image Text:Suppose that George wants to determine if the number of insects in a given area is related to the number of flowers in that area. He creates three 1 m2 quadrats in his backyard and Data point 1 X1 = 5 Yi = 17 counts the number of flowers (x) and number of insects (y) Data point 2 X2 9. Y2 = 1 in each quadrat. His data are shown in the table. Data point 3 X3 = 10 Уз = 15 Calculate the Pearson product-moment correlation Mean x = 8.00 y = 11.00 coefficient, r, using the formula Standard deviation sdx= 2.646 sdy= 8.718 E Zxi · Zyi r = п — 1 where z is the z-score for each value, x; represents the x-value for each data point, y; represents the y-value for each data point, and n represents the sample size. Complete the following five steps to calculate r, and give each of your answers precise to two decimal places. Step 1. Calculate the z-score for each x-value. X1 Zx1 = X2 Zx2 = X3 – x sd. sdx sd. Zx3 =
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