Ex: Graphical Interpretation of a Scatter Plot and Line of Best Fit

Ex: Graphical Interpretation of a Scatter Plot and Line of Best Fit


– AFTER TEST NUMBER ONE, A
TEACHER SURVEYED HER STUDENTS ABOUT HOW MANY HOURS OF TV
THEY WATCHED PER NIGHT AND COMPARED THE RESULTS
TO TEST 1 SCORES. THE RESULT ARE GIVEN BELOW. SO WHAT WE’RE SEEING BELOW
IS A SCATTER PLOT AND A LINE OF BEST FIT. THE SCATTER PLOT IS MADE UP
OF THE RED POINTS WHERE EACH POINT REPRESENTS
THE RESULTS FROM ONE STUDENT. SO FOR EACH POINT
THE X COORDINATE REPRESENTS THE NUMBER OF HOURS OF TV
THE STUDENT WATCHED PER NIGHT AND EACH Y COORDINATE REPRESENTS
THE SCORE ON TEST NUMBER 1. SO IF WE TOOK THE DATA
FROM THE SURVEY AND THEN PERFORMED
LINEAR REGRESSION THE RESULTING LINEAR EQUATION
WOULD PRODUCE THE BLUE LINE, WHICH WE CALL
THE LINE OF BEST FIT. SO THE LINE OF BEST FIT
IS THE LINE THAT BEST REPRESENTS THE GIVEN DATA. FOR THIS PROBLEM, WE’RE ASKED TO
PREDICT A STUDENT’S TEST SCORE IF THEY WATCH 1.5 HOURS OF TV
PER NIGHT. SO TO MAKE THIS PREDICTION
WE’LL USE THE LINE OF BEST FIT. SO WE’LL START BY FINDING 1.5
ON THE X AXIS WHICH REPRESENTS THE NUMBER OF
HOURS OF TV WATCHED PER NIGHT WHICH WOULD BE HERE AND WE’LL GO STRAIGHT
TO THE LINE OF BEST FIT WHICH WOULD BE HERE AND THEN ONCE WE’RE ON THE LINE
WE’LL GO STRAIGHT TO THE Y AXIS TO MAKE OUR PREDICTION. SO IT LOOKS LIKE IT’S MORE THAN
75 BUT OBVIOUSLY LESS THAN 80 AND CLOSER TO 75 THAN 80 SO WE’LL MAKE A PREDICTION
OF 76. SO BASED UPON THE LINE
OF BEST FIT, IF A STUDENT WAS TO WATCH
1.5 HOURS OF TV PER NIGHT THE PREDICTION WOULD BE
A TEST SCORE OF 76. THIS DOES NOT MEAN THAT IF A STUDENT WATCHES 1.5 HOURS
OF TV PER NIGHT THEY’LL SCORE A 76 ON THE TEST. NOTICE IF WE LOOK
AT THE ACTUAL DATA THERE’S A STUDENT RIGHT HERE THAT WATCHED 1.5 HOURS OF TV
PER NIGHT BUT ACTUALLY SCORED BELOW 60%
ON TEST 1. SO IT’S IMPORTANT TO KEEP
IN MIND THAT A PREDICTION WILL ALWAYS
HAVE A MARGIN OF ERROR. I HOPE YOU FOUND THIS HELPFUL.  

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