Which of the following is a true statement? a) a negative correlation indicates that as values of x increase, values of y will decrease. b) the coefficient of determination can assume negative values. c) the variable that is being predicted in regression analysis is the independent variable. d) if there is no correlation between the independent and dependent variables, then the value of the correlation coefficient must be -1. e) the correlation coefficient r is always greater than 1. f) none of the above

a) True

b)False

c)False

d)False

e)False

Step-by-step explanation:

Correlation is a statistical technique that help us to know relation between two variables.

a) True

it is correct to say as a negative correlation means that there is an inverse relation between the two variables.

b) False

The coefficient of determination, , can never have a negative value because it is square of coefficient of regression and a squared value can never be negative.

c)False

The variable to be determined is dependent variable and its value depend on the independent variables.

d)False

The value of correlation coefficient must be zero. A negative correlation means that there exist an inverse relation.

e)False

It ranges from -1 to 1.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.