d) State the r value, R² and the regression equation rounded to two decimal places. r = 0.96 r = Regression model (Equation) Write out the equation rounding the numbers to two decimal places.
Correlation coefficient (r) : The correlation coefficient r can be calculated using the formula, (r is known as the Pearson correlation coefficient) :
r = ∑((x–x̄)(y–ȳ))/ √[(x–x̄)2 ×(y– ȳ)2] ... (1)
Coefficient of determination (R2 or r2) :
R2 or r2is known as the coefficient of determination and can be calculated by squaring the value of correlation coefficient r i.e.,
R2 = r2 ... (2)
Regression Equation :
The regression equation between two variables x and y is given by,
y = a + bx ...(3)
Where, a is known as the intercept and b is known as the slope.
a and b are calculated as :
b = Σ((x - x̄)(y - ȳ)) /(x–x̄)2 ...(4)
And,
a = ȳ – b(x̄) ... (5)
Step by step
Solved in 6 steps
