hp calculators HP 12C Platinum Statistics - correlation coefficient The correlation coefficient HP12C Platinum correlation coefficient

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1 HP 1C Platium Statistics - correlatio coefficiet The correlatio coefficiet HP1C Platium correlatio coefficiet Practice fidig correlatio coefficiets ad forecastig

2 HP 1C Platium Statistics - correlatio coefficiet The correlatio coefficiet Statistics ca be uderstood as a set of tools ivolvig the study of methods ad procedures for collectig, classifyig, ad aalyzig data. Statistical tools also offer the meas for makig scietific ifereces from summarized data, like liear regressio ad forecastig. Both liear regressio ad forecastig are computed with the parameters that defie a curve (or lie) that best represets the sample, give the plotted data of a two-variable sample is close eough to a straight lie that it ca be represeted this way. The correlatio coefficiet r is i the rage (-1 r 1) ad measures how close the sample is to a straight lie. The closer the sample is to a straight lie, the closer r will be to 1 ad the closer the forecasted poits will be to the sample behavior. HP1C Platium correlatio coefficiet O the HP1C Platium, statistics data are stored as a set of summatios resultig from the origially collected data. The collected data set must be typed i prior to usig ay statistics features available i the HP1C Platium. The HP1C Platium memory orgaizatio allows the study of statistic data orgaized as oe- or two-variable sample. As a geeral procedure, data is always collected as a pair of umbers, or (,y ) values, ad the HP1C Platium computes the followig summatios: y ( ) ( y ) ( y ) Figure 1 With these values updated ad stored i memory, the HP1C Platium computes the correlatio coefficiet with the followig epressio: r = y ( ) ( ) y y There are also fuctios to forecast values for each of the two variables. These fuctios are associated to Q (forecast give y) ad R (forecast y give ) keys. Each time a ew forecast is calculated, the correlatio coefficiet is computed too, ad pressig ~ right after gq or gr shows its value. The HP1C Platium uses the followig epressios to compute the forecasted values: y Figure y ˆ = A + B ˆ = y A B give: y y = ad A = y B B ( ) Figure 3 hp calculators - - HP 1C Platium Statistics - correlatio coefficiet - Versio 1.0

3 HP 1C Platium Statistics - correlatio coefficiet Practice fidig the correlatio coefficiet Eample 1: A lad researcher wats to compute the relatioship betwee the costructed area ad the lad area of a commuity i order to suggest the costructio area for a ew home with a lad area of 1500 sq yards ad the suggested lad area for a costructio with 350 sq yards based o forecasted values. He also wats to kow how good this relatioship fits i a straight lie to kow if his suggestios are valid. The table below summarizes his measuremets. Lad Area (sq yards) Costructio Area (sq yards) Lad Area (sq yards) Costructio Area (sq yards) Figure 4 Solutio: Be sure to clear the statistics / summatio memories before startig the problem. f² Figure 5 The eter the first data poit. 310 \ 1000 _ Figure 6 The first etered value (costructio area) is used as the y variable ad the secod value (lad area) is used as the variable. The display shows the umber of etries each time _ is pressed. Make sure that all data is etered: 560 \ _ 90 \ _ 3300 \ _ 080 \ 9000 _ 700 \ _ 380 \ _ 3080 \ 1000 _ Figure 7 hp calculators HP 1C Platium Statistics - correlatio coefficiet - Versio 1.0

4 HP 1C Platium Statistics - correlatio coefficiet Sice the y-values are the costructio area, the forecast costructio area (y) for a 1500 sq yards lad area is computed by pressig: 1500 gr Figure 8 The correlatio coefficiet is automatically computed each time a forecastig is performed. Press: ~ Figure 9 The lad area is stored as -values, so for a 350 sq yards costructio area, the forecasted lad area is: 350 gq Figure 10 Although the correlatio coefficiet has the same value for the same sample, it's easy to check for it: ~ Figure 11 Aswer: For a costructio area of 3,50 sq yards, the estimated lad area eeded is approimately 14,140 sq yards. For a lad area of 1,500 sq yards, a costructio area of approimately 3,140 sq yards is recommeded. The sample shows a correlatio coefficiet of 0.95, so the forecast is close to the actual data. Eample : A stockholder observes the foreig stock market for some time i order to compose a curve that relates the amout of ivestmet with amout of earigs i a particular brad. He decides to aalyze the data ad use the correlatio coefficiet to measure the margi of error whe predictig the amout of earigs give the amout of ivestmet. If the correlatio coefficiet is lower tha 0.80, the he will ot use the data to make future predictios. The collected data so far is as follows: Ivestmet amout Amout of earigs Ivestmet amout Amout of earigs $1,00,000 $91,000 $1,450,000 $11,000 $1,000,000 $98,000 $1,300,000 $109,000 $900,000 $85,000 $1,150,000 $99,000 hp calculators HP 1C Platium Statistics - correlatio coefficiet - Versio 1.0

5 HP 1C Platium Statistics - correlatio coefficiet Solutio: Be sure to clear the statistics / summatio memories before startig the problem. f² Figure 1 Cosider that each pair must be etered prior to add it to the statistics summatios \ _ Figure 13 Remember that the display shows the umber of etries each time _ is pressed. Make sure that all data is etered: \ _ \ _ \ _ \ _ \ _ To compute the correlatio coefficiet, press: 1 gq ~ (Note: Ay value will do i place of the 1 show here) Figure 14 Aswer: The correlatio coefficiet for the collected data is 0.84, ad it is higher tha the stockholder defied. Therefore, the available data will be used to predict future ivestmets. hp calculators HP 1C Platium Statistics - correlatio coefficiet - Versio 1.0