A professor in the School of Business in a university polled a dozen colleagues about the number of professional meetings they attended in the past five years (x) and the number of papers they submitted to refereed journals (y) during the same period. The summary data are given as follows: n = 12, x = 4, y = 12.>f, x7 =232, Efxyi=318

a) Fit a simple linear regression model between x and y by finding out the estimates of intercept and slope.

b) Comment on whether attending more professional meetings would result in publishing more papers.

Answer:

a) SLOPE AND INTERCEPT

intercept = 37.8

slope = -6.45

b) COMMENT

Attending more professional seminars would result in publishing less papers.

Step-by-step explanation

a) SLOPE AND INTERCEPT

Best fit line is in the form y = a + bx.

From the given, we can infer the following information:

?∑x=nx? ?=12(4)=48?

??∑y=ny?? ?=12(12)=144?

The intercept a is computed using: ?a=?n∑x2−(∑x)2∑y∑x2−∑x∑xy??. Substituting the values, we get:

?a=?(12)(232)−(48)2(144)(232)−(48)(318)?? = 37.8

The slope b is computed using: ??b=?n∑x2−(∑x)2n∑xy−∑x∑y??. Substituting the values, we get:

??b=?(12)(232)−(48)2(12)(318)−(48)(144)?? = -6.45

b) COMMENT

The regression line has equation: ?y=37.8−6.45x?.

Since the slope is negative, the relationship between the number of professional meetings attended (x) and the number of published journals (y) is inverse. Meaning, attending more professional seminars would result in publishing less papers.