Find the regression equation, letting the first variable be the predictor (x) variable. Find the best predicted Nobel Laureate
1 answer:
The table is missing, so i have attached it.
Answer:
Regression equation is;
y = 0.2028x - 8.443
The predicted value is not at all close to the actual novel rate
Step-by-step explanation:
The internet users will be the x-values while the novel laureates will be the y-values.
Thus, sum of x values is;
Σx = 79.5 + 79.6 + 56.8 + 67.6 + 77.9 + 38.3 = 399.7
Sum of y values is;
Σy = 5.5 + 9 + 3.3 + 1.7 + 10.8 + 0.1
Σy = 30.4
Σx² = 79.5² + 79.6² + 56.8² + 67.6² + 77.9² + 38.3²
Σx² = 27987.71
Σy² = 5.5² + 9² + 3.3² + 1.7² + 10.8² + 0.1²
Σy² = 241.68
Σxy = (79.5 × 5.5) + (79.6 × 9) + (56.8 × 3.3) + (67.6 × 1.7) + (77.9 × 10.8) + (38.3 × 0.1)
Σxy = 2301.16
The regression line will be;
y = b1(x) + b0
b1 is expressed as;
b1 = [nΣxy - (Σx • Σy)]/[nΣx² - (Σx)²]
Where n is number of given data which is n = 6.
Thus;
b1 = [(6 × 2301.16) - (399.7 × 30.4)]/[(6 × 27987.71) - (399.7)²]
b1 = 1656.08/8166.17
b1 = 0.2028
b0 is expressed as;
b0 = [(Σy • Σx²) - (Σx • Σxy)]/[nΣx² - (Σx)²]
b0 = [(30.4 × 27987.71) - (399.7 × 2301.16)]/[(6 × 27987.71) - (399.7)²]
b0 = -68947.268/8166.17
b0 = -8.443
Thus, regression equation is;
y = 0.2028x + (-8.443)
y = 0.2028x - 8.443
Best predicted value is given as;
y¯ = (Σy)/n
y¯ = 30.4/6
y¯ = 5.067 per 10 million people.
The predicted value is far greater than the actual value of 2 per 10 million people.
Thus, we can say that the predicted value is nowhere close to the actual value
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