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- WE WANT TO PERFORM EXPONENTIAL REGRESSION TO FIND A FUNCTION
TO MODEL THE MOBILE BROADBAND TRAFFIC IN A STATE
AND THEN USE THE MODEL TO PREDICT
THE BROADBAND TRAFFIC IN 2014.
LOOKING AT THE TABLE NOTICE HOW THE FIRST YEAR GIVEN IS 2006.
THIS IS THE BASE YEAR
AND INSTEAD OF USING THE ENTIRE YEAR AS THE INPUT
WE NORMALLY LET THE BASE YEAR BE THE INPUT OF ZERO
AND THEN SINCE THE YEARS INCREASE
BY 1 WE WOULD HAVE 0, 1, 2, 3, 4 AS THE INPUTS.
SO THESE INPUTS REPRESENT THE NUMBER OF YEARS AFTER 2006
WHICH WE'LL LET EQUAL T.
THE OUTPUTS OR THE FUNCTION VALUES
WILL BE THE AMOUNT OF TRAFFIC IN TERABYTES.
SO FOR THE FIRST STEP WE WANT TO ENTER THE DATA
INTO THE CALCULATOR.
SO I'LL PRESS THE STAT KEY AND THEN ENTER.
TO SAVE SOME TIME I'VE ALREADY ENTERED THE DATA
BUT LET'S SAY FOR EXAMPLE WE HAD OLD DATA IN THE FIRST COLUMN
WHICH REPRESENTS THE INPUTS,
WE COULD GO TO THE TOP OF THE COLUMN,
PRESS CLEAR AND THEN ENTER,
AND THEN ENTER THE NEW DATA.
SO FOR HERE I'LL REENTER 0 THRU 4.
NEXT, EVEN THOUGH IT'S NOT REQUIRED
I WANT TO GRAPH A SCATTERPLOT OF THE DATA
SO WE CAN GRAPH THE MODEL RIGHT ON TOP OF THE SCATTERPLOT.
TO DO THIS WE DO HAVE TO ADJUST THE WINDOW THOUGH
SO THAT THESE VALUES WILL SHOW ON THE SCREEN.
AGAIN, I'VE ALREADY DONE THIS.
NOTICE HOW THE INPUTS FALL BETWEEN THE VALUES OF -1 AND +5
FOR THE X MIN AND MAX AND NOTICE THAT THE OUTPUTS
OR FUNCTION VALUES FALL BETWEEN -8,000 AND +70,000.
NOTICE HOW I DID MAKE THE Y MINIMUM NEGATIVE
BECAUSE I DO LIKE TO SEE THE ORIGIN ON THE COORDINATE PLANE.
TO TURN THE SCATTERPLOT ON AS LONG AS THE DATA IS IN L1 AND L2
WE CAN PRESS Y =, PRESS THE UP ARROW, PRESS ENTER ON PLOT 1,
AND THEN BACK DOWN.
NOTICE HOW IT'S NOW HIGHLIGHTED WHICH MEANS
THE SCATTERPLOT IS TURNED ON.
SO IF PRESS GRAPH HERE'S OUR SCATTERPLOT.
BUT OUR MAIN GOAL IS TO FIND THE EXPONENTIAL FUNCTION
THAT FITS THIS DATA
SO NOW WE'LL DO THAT.
WE'LL PRESS THE STAT KEY, RIGHT ARROW TO CALCULATE,
I'M GOING TO ARROW DOWN TO EXPONENTIAL REGRESSION
WHICH I BELIEVE IS NUMBER 9, NOW IT'S ZERO.
SO NOW WE'RE GOING TO PRESS ENTER AND BEFORE WE PRESS ENTER
AGAIN I DO WANT TO STORE THIS EQUATION IN Y1,
SO I'M GOING TO PRESS VARS, RIGHT ARROW ONCE, ENTER, ENTER
AND NOW THIS WILL GIVE ME THE REGRESSION FUNCTION
AS WELL AS STORE IT IN Y1.
SO NOW I'LL PRESS ENTER.
SO HERE'S THE VALUE OF "A" AND B FOR OUR EXPONENTIAL FUNCTION.
NOTICE R SQUARED THE COEFFICIENT OF DETERMINATION
IS VERY CLOSE TO ONE WHICH MEANS THIS IS A GOOD MODEL
FOR THE DATA.
LET'S GO AHEAD AND ROUND THE VALUES OF "A" AND B
TO FOUR DECIMAL PLACES FOR OUR EXPONENTIAL FUNCTION.
SO THIS WOULD GIVE US
THE EXPONENTIAL FUNCTION F OF T = 1,345.8716 x 2.8238
RAISED TO THE POWER OF T WHERE T EQUALS THE NUMBER OF YEARS
AFTER 2006 AND F OF T EQUALS THE TRAFFIC IN TERABYTES.
NOW BEFORE WE GO BACK TO THE CALCULATOR LET'S DETERMINE
THE VALUE OF T TO MAKE THE PREDICTION FOR 2014.
T IS GOING TO BE EQUAL TO 2014 MINUS THE BASE HERE OF 2006.
SO T IS EQUAL TO 8 TO MAKE THE PREDICTION FOR 2014.
SO WE NEED TO FIND F OF 8.
BUT BEFORE WE DO THIS, SINCE WE STORED THE FUNCTION IN Y1
IF WE PRESS THE GRAPH KEY WE CAN SEE THE GRAPH
OF OUR EXPONENTIAL FUNCTION RIGHT ON THE SCATTERPLOT
AND WE CAN SEE HOW WELL THE GRAPH DOES FIT THE DATA.
AND NOW TO EVALUATE THE FUNCTION AT T = 8
BECAUSE WE HAVE THE FUNCTION IN Y1 WE CAN PRESS 2nd MODE
TO GO BACK TO THE HOME SCREEN, PRESS THE VARS KEY,
RIGHT ARROW ONCE TO Y VARS, AND THEN ENTER, ENTER,
WHICH BRINGS Y1 TO THE HOME SCREEN
AND NOW WE CAN JUST ENTER 8 IN PARENTHESES
JUST LIKE FUNCTION NOTATION.
BUT WE SHOULD BE AWARE
THIS IS GOING TO USE THE FUNCTION PROVIDED HERE
WITH ALL THESE EXTRA DECIMAL PLACES.
SO IT WILL GIVE US A DIFFERENCE ANSWER
THEN IF WE USED OUR FUNCTION HERE
WHERE WE USED ROUNDED VALUES.
SO WE WILL COMPARE THE TWO FUNCTION VALUES
BUT LET'S GO AHEAD AND USE THE MORE ACCURATE ONE.
ROUNDED TO THE NEAREST TERABYTE THIS WOULD BE 5,441,359,
WHICH WOULD BE THE PREDICTION FOR THE YEAR 2014.
NOW LET'S SEE HOW DIFFERENT THIS VALUE WOULD BE
IF WE USED OUR FUNCTION TO DETERMINE THE VALUE OF F OF 8.
NOTICE HOW THERE'S A SLIGHT DIFFERENCE.
USING OUR FUNCTION WE WOULD HAVE A VALUE OF 5,440,955 TERABYTES.
SO JUST BE AWARE THERE IS A SLIGHT DIFFERENCE
BASED UPON WHICH FUNCTION WE USE.
OKAY, I HOPE YOU FOUND THIS HELPFUL.