The formula for calculating the correlation coefficient (r) is:
r = [n∑xy - (∑x)(∑y)] / √[(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)]
where n is the number of data points.
Using the given information:
n = 16
∑x = 678
∑y = 104.54
∑x^2 = 36,056
∑y^2 = 683.447
∑xy = 4,376.36
Plugging in these values into the formula, we get:
r = [16(4376.36) - (678)(104.54)] / √[(16(36056) - (678)^2)(16(683.447) - (104.54)^2)]
r = [70,021.76 - 70,824.12] / √[(579,296 - 460,084)(11,101.552 - 10,914.8516)]
r = -802.36 / √[(119,212)(186.7004)]
r = -802.36 / √(22,243,313.9)
r = -0.9781
Therefore, the correlation between temperature and milk pH is approximately -0.9781.
The correct answer is: -0.9781
The relationship between temperature and milk pH is investigated. The data in the accompanying table represent x = temperature (°C) under specified experimental conditions and y = milk pH.
°C
4 4 24 24 25 38 38 40
pH
6.85 6.79 6.63 6.65 6.72 6.62 6.57 6.52
°C
45 50 55 56 60 67 70 78
pH
6.50 6.48 6.42 6.41 6.38 6.34 6.32 6.34
The following information is known: ∑ x = 678 ∑ y =104.54 ∑ x2 = 36 056 ∑ y2 = 683.447 ∑ xy = 4376.36
Calculate the correlation between temperature and milk pH.
– 0.9781
– 0.9565
– 0.0179
0.9565
0.9889
1 answer
1 answer