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Find the correlation coefficient (r) using the data below. x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14; || y 50 55 60 61 63 66 68 70 73 74 76 78 80 83 85

User Pwdst
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Final answer:

The correlation coefficient (r) is approximately 0.835.

Step-by-step explanation:

To find the correlation coefficient (r) using the given data, we can use the formula for calculating the correlation coefficient:

r = [∑(x - mean(x))(y - mean(y))] / sqrt([∑(x - mean(x))^2] * [∑(y - mean(y))^2])

First, we need to calculate the mean of x and y:

mean(x) = Sum of all x values / Number of x values = (0+1+2+3+4+5+6+7+8+9+10+11+12+13+14) / 15 = 7

mean(y) = Sum of all y values / Number of y values = (50+55+60+61+63+66+68+70+73+74+76+78+80+83+85) / 15 = 69.33

Next, we calculate the numerator and denominator of the formula separately:

Numerator = [∑(x - mean(x))(y - mean(y))] = [(0-7)(50-69.33) + (1-7)(55-69.33) + ... + (14-7)(85-69.33)]

Denominator = sqrt([∑(x - mean(x))^2] * [∑(y - mean(y))^2]) = sqrt([(0-7)^2 + (1-7)^2 + ... + (14-7)^2] * [(50-69.33)^2 + (55-69.33)^2 + ... + (85-69.33)^2])

Plugging the values into the formula and performing the calculations, we find that the correlation coefficient (r) is approximately 0.835.

User Peter Prettenhofer
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