Toyota Company Management - Assignment Example

Toyota Company Report Student Name Student ID Date Toyota Company Report Introduction The paper below focuses on providing responses to two questions 1 & 2. Each of the questions contributes differently to the report of Toyota Company. The first question provides an analysis of the stress levels of the employee while the second focuses on the analysis of two colleges in relation to the amount of work or attendance and the impact it has on the grades of the students. Question ONE (60 marks) Two companies are comparing the stress levels of their employees for all ages. Company A has a sample of TEN employees and Company B took a sample of 14 employees. The company selected these employees and took the blood pressure at the end of the working day. The results are below Table 1: Samples of employees from two companies Company A Company B Employee  Systolic Blood Pressure Age Employee  Systolic Blood Pressure Age 1 133 37 1 128 32 2 143 39 2 135 32 3 135 42 3 140 38 4 151 44 4 147 40 5 143 47 5 153 41 6 158 48 6 154 42 7 163 50 7 160 46 8 146 51 8 160 47 9 168 52 9 162 47 10  160 54 10 164 47 11 164 48 12 165 49 13 171 49 14 175 50 Question 1Tasks 1. In the examples, which is the independent variable and which is the dependent variable? Give a detailed reason for your answers. (2 marks) Independent variable: Age Independent variable refers to that variable whose change does not depend on another. It is independent of the actions of the other variable with which comparison is made to it. In many cases, it has the ability to control the dependent variable. Dependent variable: systolic blood press A dependent variable refers to one, which relies on another variable for change. The age of the person determines their systolic blood pressure and hence systolic blood pressure existing as the dependent variable. 2. Create a scatter diagram of the relationship between the two variables. (8 Marks) 3. Calculate the strengths of relationships for both companies. Give precise details of the results. (6 marks) In calculating the strengths of the relationships between the two variables in each of the companies, correlation is used. The correlation for company A results to 0.8 while that of company B is 1 each rounded off. The results indicate that the strength of the relationship between age and systolic blood pressure of employees in company B is more positively correlated compared to that of those in company A. A change in age in company B is strongly associated with a change in systolic blood pressure of the employees. 4. What percentage of the outcomes for each company can be explained in the tests? Explain how you obtained your answer. (6 marks) 100% for company B outcomes prove explainable considering the high level of correlation between the variables. The difficulty in explaining the percentages of outcomes for company A comes from its correlation figure, which is 0.8, which represents 80% of the actual total required. 5. What is the regression equation for both companies? (8 marks) Company A Company A Employee  Systolic Blood Pressure (Y) Age (X) XY X^2 Y^2 1 133 37 4921 1369 17689 2 143 39 5577 1521 20449 3 135 42 5670 1764 18225 4 151 44 6644 1936 22801 5 143 47 6721 2209 20449 6 158 48 7584 2304 24964 7 163 50 8150 2500 26569 8 146 51 7446 2601 21316 9 168 52 8736 2704 28224 10  160 54 8640 2916 25600 Summation 1340 464 70089 21824 226286 Correlation   0.777868       Formula Used a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] Based on the above, a=[(1340)(21840)-(464)(70089)]/[10(21824)-(464)^2] a=[-3255696]/[2944} a=-1105.875 b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] b=[10(70089)-(464)(1340)]/10(21824)-(464)^2 b=79130/2944 b=26.878 Inserting the above in the equation y=a+bx y=-1105.875+26.878x Company B Company B Employee  Systolic Blood Pressure (Y) Age (X) XY X^2 Y^2 1 128 32 4096 1024 16384 2 135 32 4320 1024 18225 3 140 38 5320 1024 19600 4 147 40 5880 1024 21609 5 153 41 6273 1024 23409 6 154 42 6468 1024 23716 7 160 46 7360 1024 25600 8 160 47 7520 1024 25600 9 162 47 7614 1024 26244 10 164 47 7708 1024 26896 11 164 48 7872 1024 26896 12 165 49 8085 1024 27225 13 171 49 8379 1024 29241 14 175 50 8750 1024 30625 Summation 2178 608 95645 14336 341270 Correlation   0.976689       a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] Formula Used a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] a=[(2178)(14336)-(608)(95645)]/[14(14336)-(608)^2] a=[-26928352]/[-168960] a=159.377 b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] b=[14(95645)-(608)(2178)]/[14(14336)-(608)^2] b=[14806]/[-168960] b=-0.088 Inserting the above in the equation y=a+bx y=159.377+-0.088x 6. If each company did the same blood pressure test of one more employee who is 46 years old (both companies) what would be the expected blood pressure of the employee in each company? ( 6 marks) Company A The employee in company A would have a systolic blood pressure of 139 Company B The employee would have a systolic blood pressure of 157 7. The company wishes to suggest a limit of a Systolic Blood Pressure of 150 for each company. How old would an employee be in company A and company B? (6 marks) Company A the employee would be at 46 age based on the median age that is (44+47)/2=45.5 In company B, the systematic flow of systolic blood pressure and age proves easy to identify the age at which 150 systolic blood pressure is attained. This is at age 40. 8. Suggest a sensible range of values for employees’ ages based on the data given. ( 4 marks) Company A Least age= 37 Highest age= 54 Ranges include: 35-40, 41-45, 46-50, and 51-55 Company B Least age=32 Highest age=50 Ranges include: 31-35, 36-40, 41-45, and 46-50 9. It was decided to merge the two companies together to get an overall picture of the company. Find the correlation co-efficient, determination of co-efficient, the regression equation. (8 marks) Company A+B Employee Systolic Blood Pressure (Y) Age (X) XY X^2 Y^2 1 128 32 4096 1024 16384 2 135 32 4320 1024 18225 3 133 37 4921 1369 17689 4 140 38 5320 1444 19600 5 143 39 5577 1521 20449 6 147 40 5880 1600 21609 7 153 41 6273 1681 23409 8 135 42 5670 1764 18225 9 154 42 6468 1764 23716 10 151 44 6644 1936 22801 11 160 46 7360 2116 25600 12 143 47 6721 2209 20449 13 160 47 7520 2209 25600 14 162 47 7614 2209 26244 15 164 47 7708 2209 26896 16 158 48 7584 2304 24964 17 164 48 7872 2304 26896 18 165 49 8085 2401 27225 19 171 49 8379 2401 29241 20 163 50 8150 2500 26569 21 175 50 8750 2500 30625 22 146 51 7446 2601 21316 23 168 52 8736 2704 28224 24  160 54 8640 2916 25600 Summation 3518 1072 165734 48710 567556 Correlation 0.821563 Determination of co-efficient 0.674966 a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] Formula Used a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] a=[(3518)(48710)-(1072)(165734)]/[24(48710)-(1072)^2] a=[-6305068]/[19856] a=-317.540 b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] b=[24(165734)-(1072)(3518)]/[24(48710)-(1072)^2] b=206320/19856 b=10.391 Inserting the above in the equation y=a+bx y=-317.540+10.391x 10. Comment on how the answers in question 9 is different from the answers in question 3,4 and 5. ( 6 marks) The answer in question 9 gives a common equation combining the two companies with the correlation of 0.8 obtained compared to 0.8 for company A and 1 for company B. The correlation indicates that the correlation for company B independent of A has a closer relationship evident in the variables as of company A and the two companies combined. The equations also provide different values for the three samples that is company A, company B and company A+B. These are y=-1105.875+26.878x, y=159.377+-0.088x and y=-317.540+10.391x respectively. The above indicate the strength of the relationship between the two variables independently and combined for the three samples of companies. Question TWO (20 marks) Two colleges are analyze whether the amount of work or attendance affects the grades of students. College A did a sample of 21 students and College B did a sample of 20 students. The results are in table 2 Table 2: Sample of College students from two colleges College A College B No of absences Grade Hours studied Grade 4 53% 6 53% 3 60% 7 60% 5 56% 6.5 56% 2 79% 8 79% 4 58% 6.6 58% 2 85% 8.1 85% 3 70% 7 70% 3 56% 7 56% 3 69% 7.5 69% 4 76% 7 76% 2 79% 8 79% 3 68% 7 68% 3 74% 7.5 74% 4 72% 7.5 72% 2 84% 8 84% 3 78% 7.5 78% 4 76% 8 76% 3 65% 7 65% 2 92% 7 92% 3 80% 7 80% 4 65% Question 2 Tasks 1. Create a scatter diagram of the relationship between the two variables for each college. (4 Marks) 2. Calculate the strength of the relationship between each of the colleges. Make a valid comment about each relationship) (4 marks) The strength of the relationship between the different variables is measured using the correlation obtained. This is either negative or positive correlation. A positive correlation indicates to a strong relationship between the variables while a negative correlation indicates the opposite. For the above data, the correlation for college A and B are as below: College A Correlation for college A is -0.7, which indicates to limited existence of a relationship between the variables. College B Correlation for college B is 0.7, which indicates a positive correlation between the two sets of variables. 3. Why one of the relationships is negative and one positive? Be specific in your answers ( 4 marks) The negative and positive correlations reflect the relationship between the different variables. A positive correlation indicates that the changes in variables have an impact on the each other in tandem. A decrease in one variable as a similar impact on the other similar to an increase. An increase in the hours of studying has an increase effect on the grade. In a negative correlation, an increase in one variables results in a decrease in the other. In the collage example, an increase in the number of absence results in a decrease in the grades of the students a decrease in absence has the opposite effect on the grades. 4. What is the regression equation for both colleges? (4 marks) College A College A No of absences (X) Grade (Y) XY X^2 Y^2 4 53% 2.12 16 0.2809 3 60% 1.8 9 0.36 5 56% 2.8 25 0.3136 2 79% 1.58 4 0.6241 4 58% 2.32 16 0.3364 2 85% 1.7 4 0.7225 3 70% 2.1 9 0.49 3 56% 1.68 9 0.3136 3 69% 2.07 9 0.4761 4 76% 3.04 16 0.5776 2 79% 1.58 4 0.6241 3 68% 2.04 9 0.4624 3 74% 2.22 9 0.5476 4 72% 2.88 16 0.5184 2 84% 1.68 4 0.7056 3 78% 2.34 9 0.6084 4 76% 3.04 16 0.5776 3 65% 1.95 9 0.4225 2 92% 1.84 4 0.8464 3 80% 2.4 9 0.64 4 65% 2.6 16 0.4225 Summation 66 14.95 45.78 222 10.8703 Correlation -0.662477111 a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] Formula a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] a=[(14.95)(222)-(66)(45.78)]/[21(222)-(66)^2] a=297.42/306 a=0.972 b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] b=[21(45.78)-(66)(14.95)]/[21(222)-(66)^2] b=[-25.32]/306 b=-0.083 Inserting the above in the equation y=a+bx y=0.972+-0.083x College B College B Hours studied (X) Grade (Y) XY X^2 Y^2 6 53% 3.18 36 0.2809 7 60% 4.2 49 0.36 6.5 56% 3.64 42.25 0.3136 8 79% 6.32 64 0.6241 6.6 58% 3.828 43.56 0.3364 8.1 85% 6.885 65.61 0.7225 7 70% 4.9 49 0.49 7 56% 3.92 49 0.3136 7.5 69% 5.175 56.25 0.4761 7 76% 5.32 49 0.5776 8 79% 6.32 64 0.6241 7 68% 4.76 49 0.4624 7.5 74% 5.55 56.25 0.5476 7.5 72% 5.4 56.25 0.5184 8 84% 6.72 64 0.7056 7.5 78% 5.85 56.25 0.6084 8 76% 6.08 64 0.5776 7 65% 4.55 49 0.4225 7 92% 6.44 49 0.8464 7 80% 5.6 49 0.64 Summation 145.2 14.3 104.638 1060.42 10.4478 Correlation 0.693115 a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] Formula a=[(∑Y)(∑X^2)-(∑X)(∑XY)]/[n(∑X^2)-(∑X)^2] a=[(14.3)(1060.42)-(145.2)(104.638)]/[20(1060.42)-(145.2)^2] a=[-29.4316]/125.36 a=-0.235 b=[n(∑XY)-(∑X)(∑Y)]/[n(∑X^2)-(∑X)^2] b=[20(104.638)-(145.2)(14.3)]/[20(1060.42)-(145.2)^2] b=16.4/125.36 b=0.131 Inserting the above in the equation y=a+bx y=-0.235+0.131x 5. In part, A you were required to add the two companies together to get a bigger picture of the relationship between systolic blood pressure and age. Why is this not possible to do so in Part B with the two colleges? (4 marks) The two colleges have different variables used in explaining the relationship between grade and the absence for college A and hours spent studying and grades in college B. The common variable in this is the grades. In the part A, the common variables applied to both the two companies with each using systolic blood pressure and age. The other reasons for this are that both companies in part A had a positive correlation, which creates a meeting point. In this part, the two colleges have different levels of correlation with college A having a negative correlation and college B having a positive correlation. Read More