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Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALĖS=a+BAGE+YMIL+8ENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIlIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 MIL -0.7527 0.3586 -2.0991 ENG 4.8124 0.6196 7.7664 0.0000 Analysis of Variance Source DF s MS Regression Error 3 413.1291 138.7097 *** 0.00 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ***, ***, and “ d) Hence test whether 8 is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term "R-sq" and comment on its value.

Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALĖS=a+BAGE+YMIL+8ENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIlIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 MIL -0.7527 0.3586 -2.0991 ENG 4.8124 0.6196 7.7664 0.0000 Analysis of Variance Source DF s MS Regression Error 3 413.1291 138.7097 *** 0.00 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ***, ***, and “ d) Hence test whether 8 is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term "R-sq" and comment on its value.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 27E
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Probability Poisson distribution P(A or B) = P(A) + P(B) – P(A and B) P(A and B) = P(A) x P(B) for independent events X- Po(A) P(A and B) = P(A) x P(B|A) for dependent events P(X - x) = ** x! P(A and B) P(B|A) = P(A) Confidence Interval Normal Distribution 1. z-confidence interval: X- N(4, ơ) X-u 2. t-confidence interval: 1. Standard normal: Z - (df -n-1) 3. Confidence interval for proportion: P(1 – P) n Sampling Distribution 1. 4 =4 2. Test Statistics X-4 1. z-test for p : 2= 3. X - µ 2. t-test for u: t = (d.f. = n-1) S/ Vn Discrete Probability Distribution 3. z-test forp: z- » np 2 5 1. EÇX) = µ, = Ex,P, P(1 - P), and np z 5 (where q = 1-p) Var(X) = o = 2(x, -4,)°p, %3D %3D 4. Chi-square test statistic = y0- E) (0-E) Binomial Distribution Σ X- Bin(n, p) n-k P(X - k) - P" (1- n! p (1- n-k k!(n -k)!
Transcribed Image Text:Probability Poisson distribution P(A or B) = P(A) + P(B) – P(A and B) P(A and B) = P(A) x P(B) for independent events X- Po(A) P(A and B) = P(A) x P(B|A) for dependent events P(X - x) = ** x! P(A and B) P(B|A) = P(A) Confidence Interval Normal Distribution 1. z-confidence interval: X- N(4, ơ) X-u 2. t-confidence interval: 1. Standard normal: Z - (df -n-1) 3. Confidence interval for proportion: P(1 – P) n Sampling Distribution 1. 4 =4 2. Test Statistics X-4 1. z-test for p : 2= 3. X - µ 2. t-test for u: t = (d.f. = n-1) S/ Vn Discrete Probability Distribution 3. z-test forp: z- » np 2 5 1. EÇX) = µ, = Ex,P, P(1 - P), and np z 5 (where q = 1-p) Var(X) = o = 2(x, -4,)°p, %3D %3D 4. Chi-square test statistic = y0- E) (0-E) Binomial Distribution Σ X- Bin(n, p) n-k P(X - k) - P" (1- n! p (1- n-k k!(n -k)!
Question 4 Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALĖS-a+BAGE+YMIL+8ENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 MIL -0.7527 0.3586 -2.0991 ENG 4.8124 0.6196 7.7664 0.0000 Analysis of Variance Source DF MS F Regression 3 413.1291 138.7097 +** 0.00 Error 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ***, ****, and ** d) Hence test whether 8 is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term "R-sq" and comment on its value.
Transcribed Image Text:Question 4 Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALĖS-a+BAGE+YMIL+8ENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 MIL -0.7527 0.3586 -2.0991 ENG 4.8124 0.6196 7.7664 0.0000 Analysis of Variance Source DF MS F Regression 3 413.1291 138.7097 +** 0.00 Error 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ***, ****, and ** d) Hence test whether 8 is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term "R-sq" and comment on its value.
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