Answer True or False for the following statements. Justify your answer it False.

Question

Answer True or False for the following statements. Justify your answer it False. a. If the least-squares equation relating the independent variable x and the dependent variable y for a given problem is y = 2x + 5, then an increase of 1 unit in x is associated with an increase of 2 units in y. b. The coefficient of determination R^2 measures the variation in the dependent variable that is explained by the regression model. c. If your computed correlation coefficient is r = +1.2, then you have better than a perfect positive correlation. d. A student might expect that there is a positive correlation between the age of his or her computer and its resale value. e. In simple regression analysis, if the slope of the line is positive, then there is a positive correlation between the dependent variable y and the independent variable x. f. The coefficient of determination can assume negative values. g. A negative correlation indicates that as values of x are increased, values of y will decrease. h. If there is no correlation between the independent and dependent variables, then the value of the correlation coefficient must be -1.

Explanation / Answer

Ans:

a)True

As,slope is 2,so if we increase one unit of x,it will increase 2 units of y.

b)True

It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

c)false

r varies between -1 to 1.

d)false

(resale vaue may decrease with increase of age,so negative correlation)

e)True

f)False

Cofficient of determination,R2 is always +ve,as it is square of correlation cofficiet r.

g)True

h)False

If there is no correlation between x and y,then r=0

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