When we standardize the values of a variable, the distribution of standardized values has a mean $0$and a standard deviation $1$Suppose we measure two variables $X$and $Y$on each of several subjects. We standardize both variables and then compute the least-squares regression line. Suppose the slope of the least-squares regression line is $-0.44$We may conclude that

(a) the correlation will be $1/-0.44$

(b) the intercept will also be $-0.44$

(c) the intercept will be $1.0$

(d) the correlation will be $1.0$

(e) the correlation will also be $-0.44$

(a) $1/0.44$ will be the correlation.

(b) the intercept will be $0.44$ as well.

(c) $1.0$ will be the intercept.

(d) There will be a $1.0$ correlation.

(f) the correlation will be $0.44$ as well.

A regression line is a straight line that depicts the relationship between an explanatory variable $x$ and a response variable $y$ By entering any value of $x$ into the equation of the line, you may use a regression line to anticipate the value of $y$ for any value of $x$

The least-square regression slope is defined as follows: $b=r\frac{s_X}{s_Y}$

Substituting the standard deviations of standardized $X$ and Y variables, we get $b=r$since $s_X=s_Y=1$

In other words, the correlation is equal to the slope.

The slope of the least-squares regression line is $-0.44$ in this case. We can then deduce that the correlation is also $-0.44$

Therefore, the conclusion will be the correlation which is $-0.44$