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

Step-by-step explanation:

Hello!

a) The coefficient of determination can assume negative values.

FALSE

The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variable(s). It takes values in the range from 0 to 1, where 0 indicates that the explanatory variable has nothing to do with the variability of the dependent variable and 1 indicates that all the variability of the dependent variable is due to the explanatory variable. The closer the coefficient is to 1, the better the regression model.

b) A negative correlation indicates that as values of x decrease, values of y will decrease.

FALSE

The linear correlation analysis studies the association between two variables X and Y. A negative linear correlation means that when you draw the linear association the slope of it will be negative. A negative slope indicates that every time X increases, Y will decrease. (see example attached)

c) If there is no correlation between the independent and dependent variables, then the value of the correlation coefficient must be -1.

FALSE

This coefficient gives an idea of the degree of correlation between the variables.

If ρ = 0 then there is no linear correlation between X and Y Graphically, the slope is cero

If ρ < 0 then there is a negative association between X and Y (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.

If ρ > 0 then there is a positive association between X and Y (i.e. Both variables increase and decrease together)

d) The variable that is being predicted in regression analysis is the dependent variable.

TRUE

The dependent variable, Y, is the variable that is expected to change when the researcher manipulated the independent variable(s).

e) The correlation coefficient r is always greater than 1.

FALSE

The coefficient r takes values between -1 and 1

I hope it helps!

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752