For science class, a student recorded the high and low temperatures, in Fahrenheit, over a ten day period in September. The data
is shown in the table. Low Temperature, x 26 28 30 32 34 35 37 38 41 45
High Temperature, y 49 50 57 54 60 58 64 66 63 72
A) What is the correlation for a linear model of this data? Round to the nearest hundredth.
r =
B) Ten high and low temperatures in October are recorded and have a correlation coefficient of 0.89. In which month is there a stronger correlation between the high and low temperatures? Explain your answer.
In a graphing calculator, we enter the data. The low temperature will be entered as the independent variable and the high temperature will be entered as the dependent.
Running a linear regression on the data, we get a correlation coefficient, r, of 0.94775 ≈ 0.95.
Since the correlation coefficient for October is 0.89, while that of September is 0.95, the correlation for September is stronger than that of October. The closer the correlation coefficient is to 1, the stronger the relationship.
Thee correlation factor formula for two variables is (r) =[ nΣxy – (Σx)(Σy) / Sqrt([nΣx^2 – (Σx)^2][nΣy^2 – (Σy)^2])].
A). as per the formula the correlation factor for the given data is 0.94.
B). the month of September has the highest correlation as 0.94 is much closer to 1 than 0.89.( note: 1 denotes the perfect correlation and 0 denotes no correlation at all)
