Answer:

Trend lines are used in statistics to represent the general direction of a set of data. They are calculated by finding the line that best fits the data points. In this question, we are given two trend lines and asked to find the trend line with 1971 as origin.

Calculating the Trend Line with 1971 as Origin:

To calculate the trend line with 1971 as origin, we need to adjust the equation for the trend line with 1975 as origin. We can do this by subtracting the value of the trend line at 1971 from the value of the trend line at 1975. This will give us the slope of the line between 1971 and 1975.

To find the value of the trend line at 1971, we can substitute X = 1971 into the equation for the trend line with 1975 as origin:

Y = 20.6 + 1.68X
Y = 20.6 + 1.68(1971)
Y = 20.6 + 3311.28
Y = 3331.88

So the value of the trend line with 1975 as origin at 1971 is 3331.88.

To find the value of the trend line with 1975 as origin at 1975, we can substitute X = 1975 into the equation:

Y = 20.6 + 1.68X
Y = 20.6 + 1.68(1975)
Y = 20.6 + 3321
Y = 3341.6

So the value of the trend line with 1975 as origin at 1975 is 3341.6.

Now we can find the slope of the line between 1971 and 1975:

Slope = (Y2 - Y1) / (X2 - X1)
Slope = (3341.6 - 3331.88) / (1975 - 1971)
Slope = 9.72 / 4
Slope = 2.43

Finally, we can use the slope and the value of the trend line at 1971 to calculate the equation for the trend line with 1971 as origin:

Y = mx + b
Y = 2.43X + 3331.88 - (2.43)(1971)
Y = 2.43X - 4783.73

Therefore, the answer is d. Y = 2.43X - 4783.73.

B