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.