Using the data table below, calculate the following: linear correlation coeffici

Question

Using the data table below, calculate the following: linear correlation coefficient - r (Pearson's Product Moment) scatter diagram regression line formula -- slope-intercept form analysis of results A farmer notices that crickets seem to chirp faster on warm days. The accompanying table lists the number of chirps made by a cricket in 1 minute, along with the corresponding temperature (degrees Fahrenheit). r = n (Sigma xy) - (Sigma x) (Sigma y)/Squareroot n(Sigmax^2) - (Sigma x)^2 Squareroot n(Sigma y^2) - (Sigma y)^2 r = 10(51374) - (831)(595)/(Squareroot 10(74397) - (690541)) Squareroot 10(35911) - (354025)

Explanation / Answer

a)

XY , X2 and Y2 as it was done in the table below.

the sum of every column to get:

X=831 , Y=595 , XY=51374 , X2=76397 , Y2=35911

Use the following formula to work out the correlation coefficient.

r = 0.9987

b)

c)

XY and X2 as it was done in the table below.

the sum of every column:

X=831 , Y=595 , XY=51374 , X2=76397

Use the following equations to find a and b:

a = 37.65

b = 0.26

y = 37.65 + 0.26x

d) the conclusion will be they have a linear relationship

X Y XY XX YY   66 55 3630 4356 3025 58 53 3074 3364 2809 94 62 5828 8836 3844 120 70 8400 14400 4900 83 59 4897 6889 3481 119 69 8211 14161 4761 121 69 8349 14641 4761 65 55 3575 4225 3025 55 52 2860 3025 2704 50 51 2550 2500 2601

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