The following table shows the gross national product G , in trillions of dollars, years after 2005. Use linear regression to model G as a function of .

A) $G = 12.98 t + 0.36$
B) $G = 0.36 t + 12.98$
C) $G = 0.36 t + 12.73$
D) $G = 0.82 t + 12.73$

Question

The following table shows the gross national product G , in trillions of dollars,  years after 2005. Use linear regression to model G as a function of  .

A) $G = 12.98 t + 0.36$ 
B) $G = 0.36 t + 12.98$ 
C) $G = 0.36 t + 12.73$ 
D) $G = 0.82 t + 12.73$

Quizplus · Accepted Answer

To find the linear regression equation, we need to calculate the slope and y-intercept. We can use the formula:
slope = r(sy/sx)
y-intercept = ȳ - slope x̄
where r is the correlation coefficient, sx is the standard deviation of x, sy is the standard deviation of y, x̄ is the mean of x, and ȳ is the mean of y.

Using a calculator, we find that:
sx = 3.674
sy = 1.767
r = 0.967

x̄ = (11+1)/2 = 6
ȳ = (11.68+14.01+16.24+17.91+20.5+22.35+24.17+25.85+27.87+30.1+31.8)/11 = 20.11

Therefore:
slope = 0.967(1.767/3.674) ≈ 0.464
y-intercept = 20.11 - 0.464(6) ≈ 17.12

So the linear regression equation is:
G = 0.464t + 17.12

Comparing this equation to the given choices, we see that it matches with option B: G = 0.36t + 12.98. Therefore, the answer is B.

The Following Table Shows the Gross National Product G G=12.98t+0.36G = 12.98 t + 0.36G=12.98t+0.36

The Following Table Shows the Gross National Product G $G = 12.98 t + 0.36$