Calculate the Pearson’s correlation coefficient
Assessed value (R’000) Selling price
(R’000)
116 185
160 246
144 236
103 162
205 300
To calculate the Pearson’s correlation coefficient, you need to follow these steps:
Step 1: Calculate the mean (average) of both variables.
Assessed value (R’000) mean = (116 + 160 + 144 + 103 + 205) / 5 = 144.8
Selling price (R’000) mean = (185 + 246 + 236 + 162 + 300) / 5 = 225.8
Step 2: Calculate the deviation from the mean for each data point of both variables.
For the Assessed value (R’000):
116 - 144.8 = -28.8
160 - 144.8 = 15.2
144 - 144.8 = -0.8
103 - 144.8 = -41.8
205 - 144.8 = 60.2
For the Selling price (R’000):
185 - 225.8 = -40.8
246 - 225.8 = 20.2
236 - 225.8 = 10.2
162 - 225.8 = -63.8
300 - 225.8 = 74.2
Step 3: Calculate the product of the deviation of both variables for each data point.
For each data point, multiply the deviation of the Assessed value with the deviation of the Selling price.
-28.8 * -40.8 = 1175.104
15.2 * 20.2 = 307.04
-0.8 * 10.2 = -8.16
-41.8 * -63.8 = 2668.84
60.2 * 74.2 = 4462.84
Step 4: Sum up all the products from Step 3.
Sum of the products = 1175.104 + 307.04 - 8.16 + 2668.84 + 4462.84 = 9505.76
Step 5: Calculate the sums of squares for each variable.
For the Assessed value (R’000):
(-28.8)² + 15.2² + (-0.8)² + (-41.8)² + 60.2² = 11110.48
For the Selling price (R’000):
(-40.8)² + 20.2² + 10.2² + (-63.8)² + 74.2² = 20107.08
Step 6: Calculate the square root of the sums of squares for each variable.
Assessed value (R’000) sqrt = √11110.48 = 105.39
Selling price (R’000) sqrt = √20107.08 = 141.83
Step 7: Multiply the square roots of the sums of squares for each variable.
105.39 * 141.83 = 14943.58
Step 8: Divide the sum of the products from Step 4 by the result of Step 7.
Pearson’s correlation coefficient = 9505.76 / 14943.58 = 0.636 or 63.6% (approximately)
Therefore, the Pearson’s correlation coefficient for the given data set is 0.636 or 63.6% (approximately), which indicates a moderately positive correlation between the assessed value and selling price.