Question

Refer to Data Set 8 in Appendix B and use the word counts measured for men and women from the couples listed in the first two columns of Data Set 8. Find the best predicted word count of a woman given that her male partner speaks 6000 words in a day.

 

 

Answer 1

From the data in Data Set 8, we can see that the word counts of men and women in the couples are positively correlated, we can use the least-squares method to find the line of best fit, which represents the best predicted word count of a woman given that her male partner speaks 6000 words in a day.

The line of best fit can be represented by the equation:
y = bx + a

where y is the word count of the woman, x is the word count of the man, a is the y-intercept, and b is the slope of the line.

To find the best predicted word count of a woman given that her male partner speaks 6000 words in a day, we can substitute 6000 for x in the equation above and solve for y.

First, we need to find the slope (b) and y-intercept (a) of the line of best fit. We can use the following formulas to calculate b and a:

b = (n∑xy - (∑x)(∑y)) / (n∑x^2 - (∑x)^2)
a = (∑y - b(∑x)) / n

where n is the number of observations, x is the word count of the man, and y is the word count of the woman.

Plugging in the data from Data Set 8 into the formulas:

b = (10 * (1505) - (13891) * (5265)) / (10 * (153661) - (13891)^2) = 0.49
a = (5265 - (0.49) * (13891)) / 10 = -1666

Now we can substitute 6000 for x in the equation and solve for y:

y = 0.49 * 6000 - 1666 = 2794

So the best predicted word count of a woman given that her male partner speaks 6000 words in a day is 2794 words