The size and sale prices for six homes are given in the table. Which correlation coefficient is the only realistic value for the correlation between the sizes of these homes and their sale prices?
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Answers
Answer:
Definition of sales price in the Financial Dictionary - by Free online English dictionary and encyclopedia. What is sales price? Meaning of ...
The correlation coefficient r of the given data is 0.981.
Given:
the size and sales prices of 6 houses as shown in the image above
To find:
the correlation coefficient
Solution:
we know that the correlation coefficient r is calculated as:
r = Σ(x - X)(y - Y) ÷ {√Σ(x - X)² Σ(y - Y)²}
where X and Y are the means of x and y values respectively
the mean home size will be = (1200 + 1350 + 1720 + 1510 + 1440 + 1675)/6
X = 1482.5
the mean selling price will be = (223 + 298 + 427 + 375 + 310 + 402)/6
Y = 339.16
⇒ Σ(x - X)(y - Y) = {(1200 - 1482.5)(223 - 339.16) + (1350 - 1482.5)(298 - 339.16) + (1720 - 1482.5)(427 - 339.16) + (1510 - 1482.5)(375 - 339.16) + (1440 - 1482.5)(310 - 339.16) + (1675 - 1482.5)(402 - 339.16)
= 32815.2 + 5453.7 + 20862 + 985.6 + 1239.3 + 12096.7
= 73452.5
similarly, Σ(x - X)² = (1200 - 1482.5)² + (1350 - 1482.5)² + (1720 - 1482.5)² + (1510 - 1482.5)² + (1440 - 1482.5)² + (1675 - 1482.5)²
= 79806.25 + 17556.25 + 56406.25 + 756.25 + 1806.25 + 37056.25
= 193387.5
and Σ(y - Y)² = (223 - 339.16)² + (298 - 339.16)² + (427 - 339.16)² + (375 - 339.16)² + (310 - 339.16)² + (402 - 339.16)²
= 28986.83
⇒ r = 73452.5 ÷ √(193387.5 × 28986.83)
r = 73452.5 ÷ 74871.15
r = 0.981
Thus, the correlation coefficient r of the given data is 0.981.
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