Question

Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Find the best predicted Nobel Laureate rate for a country that has 78.8 Internet users per 100 people. How does it compare to the​ country's actual Nobel Laureate rate of 2 per 10 million​ people

Answer 1

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