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- IN THIS QUESTION,
WE'RE ASKED TO MATCH EACH SCATTERED PLOT SHOWN
WITH ONE OF THE FOUR SPECIFIED CORRELATIONS GIVEN HERE BELOW.
BEFORE WE DO THIS THOUGH,
LET'S REVIEW THE DEFINITION OF THE CORRELATION COEFFICIENT.
THE CORRELATION COEFFICIENT IS A VALUE R
SOMEWHERE IN THE CLOSED INTERVAL FROM -1 TO +1
WHERE IF R IS POSITIVE OR GREATER THAN ZERO
THIS SUGGEST A POSITIVE INCREASING LINEAR RELATIONSHIP.
AND IF R IS NEGATIVE OR LESS THAN ZERO
THIS SUGGEST A NEGATIVE
OR DECREASING LINEAR RELATIONSHIP.
THE CLOSER THE VALUE IS TO ZERO THE MORE SCATTERED THE DATA.
AND THE CLOSER THE VALUE IS TO 1 OR -1
THE LESS SCATTERED THE DATA.
SO GOING BACK TO OUR FOUR SCATTERED PLOTS,
I THINK IT'S PRETTY EASY TO SEE THAT THESE TOP TWO SCATTER PLOTS
ARE LESS SCATTERED,
AND THEREFORE THE CORRELATION COEFFICIENTS
WOULD BE CLOSER TO EITHER -1 OR +1.
LET'S SKETCH A LINE OVER THE SCATTERED PLOT
THAT WOULD REPRESENT THE DATA.
SO FOR THE FIRST SCATTERED PLOT,
THE LINE THAT REPRESENTS
THE DATA MIGHT LOOK SOMETHING LIKE THIS.
THE LINE THAT REPRESENTS THIS SCATTERED PLOT HERE
MIGHT LOOK SOMETHING LIKE THIS.
NOTICE THIS FIRST LINE IS INCREASING,
MEANING AS X INCREASES Y INCREASES,
OR IT HAS A POSITIVE SLOPE.
AND, THEREFORE, THE CORRELATION COEFFICIENT
WOULD BE CLOSER TO +1.
SO A GOOD CHOICE FOR THE CORRELATION COEFFICIENT
FOR THIS SCATTERED PLOT WOULD BE (A, 0.86).
NOTICE HOW IF WE SELECTED +0.17
THE SCATTERED PLOT WOULD HAVE TO BE MORE SCATTERED
BECAUSE ITS VALUE IS CLOSER TO ZERO.
LOOKING AT THE SCATTERED PLOT HERE,
AGAIN, NOTICE HOW THE LINE HAS A NEGATIVE SLOPE
WHERE THE RELATIONSHIP IS DECREASING.
AS X INCREASES THE Y VALUES DECREASE.
AND BECAUSE IT'S NOT VERY SCATTERED
THE CORRELATION COEFFICIENT WOULD BE CLOSE TO -1.
SO LOOKING AT OUR CHOICES HERE,
THE BEST CHOICE WOULD BE (C, -0.89).
NOW, LOOKING AT THE REMAINING TWO SCATTER PLOTS,
NOTICE HOW THE DATA IS MORE SCATTERED,
WHICH MEANS THE CORRELATION COEFFICIENT
WOULD BE CLOSER TO ZERO.
BUT, AGAIN, LET'S GO AHEAD
AND SKETCH A LINE TO REPRESENT THE DATA.
LOOKING AT THIS SCATTERED PLOT,
THE TREND DOES SEEM TO BE DECREASING AS X INCREASES.
SO LINEAR EQUATION AND MODEL THIS DATA
MIGHT LOOK SOMETHING LIKE THIS,
WHERE NOTICE HOW THE SLOPE IS NEGATIVE
OR THE LINEAR FUNCTION IS DECREASING.
AND LOOKING AT THIS SCATTERED PLOT HERE,
AGAIN, IT'S VERY SCATTERED,
BUT THE GENERAL TREND DOES SEEM TO BE UPWARD
IN THIS DIRECTION HERE.
SO BECAUSE THIS LINE HAS A NEGATIVE SLOPE,
WELL, THE DATA TENDS TO BE DECREASES AS X INCREASES.
THE CORRELATION COEFFICIENT WOULD BE NEGATIVE,
BUT BECAUSE IT'S SCATTERED IT WOULD BE CLOSE TO ZERO.
SO THE BEST CHOICE IS (B, -0.16).
AND THEN FOR THE LAST SCATTERED PLOT,
AGAIN, THE DATA IS SCATTERED,
BUT THE DATA DOES TEND TO BE INCREASING AS X INCREASES.
THE LINE HAS A POSITIVE SLOPE,
AND THEREFORE THE CORRELATION COEFFICIENT WOULD BE (D, 0.17).
I HOPE YOU FOUND THIS HELPFUL.