Question

3. A regression analysis of a data set yielded the Least Squares regression line: y = 15.8 − 0.7 x.

(a) What would be the estimated mean of Y when X = 9?

(b) A student said: “ If we plug x = 10 in the equation of the regression line, then we get an estimate for the value of Y.” What is wrong with this statement?

(c) By how much, and in what direction, would you expect Y to change if X increases by 2.5? Is this a guaranteed change?

(d) If you are told that an observed value of Y came out to be 11.46, what is your best guess for the value of X that was used in that observation?

(e) If you are told that Y cannot take negative values, what does it imply about the scope of the study, namely the range of X-values?

Answer 1

A regression analysis of a data set yielded the Least Squares regression line: y = 15.8 − 0.7 x.

a) The estimated mean of Y when X = 9 is

y = 15.8 − 0.7*9 = 9.5

b) A student said: “ If we plug x = 10 in the equation of the regression line, then we get an estimate for the value of Y.”

There is not wrong with this statement.

c) If we x increases by 2.5 then expected y decreases by 0.7*2..5 = 1.75

There is a negative direction.

d) If you are told that an observed value of Y came out to be 11.46, we have to find the value of x.

The regression equation is y = 15.8 − 0.7*x

=> 11.46 = 15.8 - 0.7*x

=> 11.46-15.8 = - 0.7*x

=> - 4.34 = - 0.7*x

=> x = 6.2