Correlation regression and Chi square

1). what advice is provided by the after amount of the pearson correlation?             Pearson alternation is a admeasurement of the amount of affiliation amid two variables. The amount of affiliation becomes stronger as it approaches the ethics 1 and -1. It additionally advance article about the administration of the association, whether it is bottomward or upward. 2). in the afterward data, there are three array (x, y, and z) for anniversary of the n =5 individuals. a. Sketch a blueprint assuming the accord amid X and Y, compute the Pearson alternation amid X and Y. Pearson alternation (r) = (?XY - (?X?Y/N))/(?(?X2-(?X)2/N)(?Y2-(?Y)2/N) = (36-(10*15)/5)/(?(30-100/5)(55-(225/5)) = (36-30)/(?(30-20)(55-45)) = 6/(?(10*10)) = 6/10 = 0.6 b. Sketch a blueprint assuming the accord amid Y and Z. compose the pearson alternation amid Y and Z. Pearson alternation (r) = (?YZ - (?Z?Y/N))/(?(?Z2-(?Z)2/N)(?Y2-(?Y)2/N) = (66-(20*15)/5)/(?(90-(400)/5)(55-(225/5)) = (66-60)/(?(90-80)(55-45)) = 6/(?(10*10)) = 6/10 = 0.6 c. Accustomed the aftereffect of genitalia A and B, what would you adumbrate for the alternation amid X and Z?             The Pearson alternation in genitalia A and B are equal. Again we would adumbrate that the alternation amid X and Z are the aforementioned with genitalia A and B. d. Sketch a blueprint assuming the accord amid X and Z. compute the Pearson alternation for these data. Pearson alternation (r) = (?XZ - (?X?Z/N))/(?(?X2-(?X)2/N)(?Z2-(?Z)2/N) = (38-(10*20)/5)/(?(30-100/5)(90-(400)/5)) = (38-40)/(?(30-20)(90-80)) = -2/(?(10*10)) = -2/10 = -0.2 e. What accepted cessation can you accomplish apropos accord amid correlations? If X is accompanying to Y and Y is accompanying to Z, does this necessarily beggarly that X is accompanying to Z?             Transitivity is not applicative accord amid correlations. When one speaks of transitivity, this alone agency that for any variables a, b and c, if a = b and b = c again a = c. This analogue is not applicative to correlations of variables. One cannot adumbrate alternation amid two variables based from correlations of alternative set of variables. For example, X is accompanying to Y, and Y is accompanying to Z. Then, one cannot adumbrate or say that X is accompanying to Z based on the accustomed correlations. 3) Sketch a blueprint assuming the band for the blueprint Y=2x-3 on the aforementioned graph, appearance the band for Y= -2x+8 4) A set of array produces a corruption blueprint of F=7x-2. Use the blueprint to acquisition the predicted amount of Y for anniversary of the afterward X scores: 0, 2, 5, 8, 10 F = 7x – 2 F(0) = 7(0) – 2 = 0 – 2 = -2 F(2) = 7(2) – 2 = 14 – 2 = 12 F(5) = 7(5) – 2 = 35 – 2 = 33 F(8) = 7(8) – 2 = 56 – 2 = 54 F(10) = 7(10) – 2 = 70 – 2 = 68 5) For the afterward data: a. acquisition the corruption blueprint for admiration Y from X ? = bX + A b = r(Sy/Sx), area r is the pearson correlation, Sy and Sx are the accepted aberration of Y and X. r = (?XY - (?X?Y/N))/(?(?X2-(?X)2/N)(?Y2-(?Y)2/N) = (170-(25*30)/5)/(?(135-(625)/5)(346-(900)/5)) = (170-150)/(?(135-125)(346-180)) = (20)/?(10)(166) = 20/?1660 = 20/40.7431 = 0.4909 b = 0.4909(6.4420/1.5811) = 2.0001 A = My – bMx = 6 – 2.0001(5) = 6 – 10.0005 = -4.0005 ? = 2.0001X – 4.0005 b. use the corruption blueprint to acquisition a predicted Y for anniversary X ? = 2.0001X –  4.0005 X ? 7 10.0002 5 6.0000 6 8.0001 3 1.9998 4 3.9999 c. acquisition the aberration amid the absolute Y amount and the predicted Y amount for anniversary individual, aboveboard the differences, and add the boxlike ethics to access SSresidual. ? Y Y - ? (Y - ?)2 10.0002 16 5.9998 35.9976 6.0000 2 -4.0000 16.0000 8.0001 1 -7.0001 49.0014 1.9998 2 -0.0002 0.0000 3.9999 9 5.0001 25.0010 SSresidual = ?(Y – ?)2 = 126 d. account the Pearson alternation for these data. Use r² and SS? to compute SSresidual, with blueprint 15.13. You should access the aforementioned amount as in allotment c. r = (?XY - (?X?Y/N))/(?(?X2-(?X)2/N)(?Y2-(?Y)2/N) = (170-(25*30)/5)/(?(135-(625)/5)(346-(900)/5)) = (170-150)/(?(135-125)(346-180)) = (20)/?(10)(166) = 20/?1660 = 20/40.7431 = 0.4909 SSy = ?(Y – ?)2 = 166 SSresidual = (1 – r2)SSy = (1 – 0.49092)(166) = (1 – 0.2410)(166) = (0.759)(166) = 125.994 or 126 Chapter 16. 6) A assistant noticed that the assembly on the academy apprentice government abide of 31 males and alone 9 females. The accepted academy citizenry on the alternative hand, consists of 55% females and 45% males. Is the gender administration for apprentice government assembly decidedly altered from the administration for the population? Test at the 0.5 akin of significance. Null Hypothesis: The gender administration for apprentice government assembly is not decidedly altered from the administration for the population. Alternative: The gender administration for apprentice government assembly is decidedly altered from the administration for the population. Observed Expected Male 31 18 Female 9 22 X2 (computed)= ?(observed – expected)2/(expected) = (31-18)2/18 + (9-22)2/22 = 9.3889 + 7.6818 = 17.0707 X2 (critical)  = 3.841 Decision rule, adios absent antecedent if X2 ? 3.841. Otherwise, abort to adios the absent hypothesis. At a = 0.05, X2 = 17.0707 ? 3.841, again we adios the absent hypothesis. We are 95% assured that the gender administration for apprentice government assembly is decidedly altered from the administration for the population. 7) Abstracts from the administration of motor cartage announce that 80% of all accountant drivers are earlier than 25. a. In a sample of n= 50 bodies who afresh accustomed dispatch tickets, 32 were earlier than 25 years and the alternative 18 were age 25 or younger. Is the age administration for this sample decidedly altered from the administration for the citizenry accountant divers? Use ? =.05. Null Hypothesis: The age administration for this sample is not decidedly altered from the administration for the citizenry accountant divers. Alternative: The age administration for this sample is not decidedly altered from the administration for the citizenry accountant divers. Licensed Drivers Observed Expected > 25 years old 32 40 ? 25 years old 18 10 X2 (computed)= ?(observed – expected)2/(expected) = (32-40)2/40 + (18-10)2/10 = 1.6 + 6.4 = 8 X2 (critical)  = 3.841 Decision rule, adios absent antecedent if X2 ? 3.841. Otherwise, abort to adios the absent hypothesis. At a = 0.05, X2 = 8 ? 3.841, again we adios the absent hypothesis. We are 95% assured that the age administration for this sample is decidedly altered from the administration for the citizenry accountant divers. b. In a sample of n=50 bodies who afresh accustomed parking tickets. 38 were earlier than 25 years and the alternative 12 were age 25 or younger. Is the age administration for this sample decidedly altered from the administration for the citizenry of accountant drivers? Use ? =.05. Null Hypothesis: The age administration for this sample is not decidedly altered from the administration for the citizenry accountant divers. Alternative: The age administration for this sample is not decidedly altered from the administration for the citizenry accountant divers. Licensed Drivers Observed Expected > 25 years old 38 40 ? 25 years old 12 10 X2 (computed)= ?(observed – expected)2/(expected) = (38-40)2/40 + (12-10)2/10 = 0.1 + 0.4 = 0.5 X2 (critical)  = 3.841 Decision rule, adios absent antecedent if X2 ? 3.841. Otherwise, abort to adios the absent hypothesis. At a = 0.05, X2 = 0.5 ? 3.841, again we abort to adios the absent hypothesis. We are 95% assured that the age administration for this sample is not decidedly altered from the administration for the citizenry accountant divers. 8) A researcher acquired a accidental sample of n = 60 acceptance to actuate whether there were any cogent preferences amid three arch brands of colas. Anniversary apprentice tasted all the brands and again called his or her favorite. The consistent abundance administration is as follows: BRAND A BRAND B BRAND C 28 14 18 Are the abstracts acceptable to announce any preferences amid the three brands? Test with ? =.05. Null hypothesis:  There are no cogent preferences amid three arch brands of colas. Alternative: There are cogent preferences amid three arch brands of colas. Brand Observed Expected A 28 20 B 14 20 C 18 20 X2 (computed)= ?(observed – expected)2/(expected) = (28-20)2/20 + (14-20)2/20 + (18-20)2/20 = 3.2 + 1.8 + 0.2 = 5.2 X2 (critical)  = 5.991 Decision rule, adios absent antecedent if X2 ? 5.991. Otherwise, abort to adios the absent hypothesis. At a = 0.05, X2 = 5.2 ? 5.991, again we abort to adios the absent hypothesis. We are 95% assured that there are no cogent preferences amid three arch brands of colas. 9) A amusing analyst suspects that bodies who serve on juries tends to be abundant earlier than citizens in the accepted population. Jurors are called from the account of registered voters, so the ages for jurors should accept the aforementioned administration as the ages for voters. The analyst obtains voters allotment annal and finds that 20% of registered voters are amid 18 and 29 years old, and 35% are age 50or older. The analyst additionally monitors board agreement over several weeks and observes the afterward administration of ages for absolute juries. Age categories for jurors 18-29 30-49 50 and over 12 36 32 Are the abstracts acceptable to achieve that the age administration for the jurors is decidedly altered from the administration for the citizenry of registered voters? Test with ? =.05. Null hypothesis: The age administration for the jurors is not decidedly altered from the administration for the citizenry of registered voters. Alternative: The age administration for the jurors is not decidedly altered from the administration for the citizenry of registered voters Age Observed Expected 18-29 12 16 30-49 36 36 50 and over 32 28 X2 (computed)= ?(observed – expected)2/(expected) = (12-16)2/16 + (36-36)2/36 + (32-28)2/28 = 1 + 0 + 0.5714 = 1.5714 X2 (critical) = 5.991 Decision rule, adios absent antecedent if X2 ? 5.991. Otherwise, abort to adios the absent hypothesis. At a=0.05, X2 = 1.5714 ? 5.991. Thus, we abort to adios the absent hypothesis. We are 95% assured that the age administration for the jurors is not decidedly altered from the administration for the citizenry of registered voters. 10) A attitude assistant is aggravating to adjudge which test-book to use for abutting year’s anterior class. To advice accomplish the decision, the assistant asks the accepted acceptance to accomplish to analysis three texts and analyze which one they prefer. The administration alternative for the accepted chic is as follows: Book 1 book 2 book 3 52 41 27 Do the abstracts announce any cogent preferences amid the three books? Test with ? =.05. Null hypothesis: There are no cogent preferences amid the three books. Alternative: There are cogent differences amid the three books. Book Observed Expected 1 52 40 2 41 40 3 27 40 X2 (computed)= ?(observed – expected)2/(expected) = (52-40)2/40 + (41-40)2/40 + (27-40)2/40 = 3.6 + 0.025 + 4.225 = 7.85 X2 (critical) = 5.991 Decision rule, adios absent antecedent if X2 ? 5.991. Otherwise, abort to adios the absent hypothesis. At a=0.05, X2 = 7.85 ? 5.991. Thus, we adios the absent hypothesis. We are 95% assured that there are cogent differences amid the three books.

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