Abraham Lincoln to a Proposed

¶ … Abraham Lincoln to a proposed survey questionnaire has indicated he had not received a grade school diploma. When a researcher correlated the information to the expected variables, he found the data did not highly correlate to the expectations derived from the data. There are many possible problems and we will discuss some of them.

Lincoln could have lied on the survey to provide a false indication of his education. He could have received the grade school diploma, which would mean the data is in error. This speaks to the issue of poor quality data and the need to have high quality and very specific data on which to base a forecast, prediction, or expected variable. Lincoln may have pursue his educational goals outside the realm of the classroom. So although lacking what he perceives to be a formal education as ruled by the state at the time, he educated himself on his own interests and therefore the survey is invalid.

The survey questionnaire is an example of the use of nominal data or data that is non-numerical. This qualitative data is subjective and open to interpretation and does not measure for the environmental variable yet the environmental effect may show up in the error statistic. Given the problem of the small sample size, this may the case. The probability for a greater measure in error measured as the t-statistic is higher as the size of the sample decreases

The lack of identifying the environmental variables that were important to Lincoln's education is critical to the wrong bivariate analysis and prediction. Lincoln likely, was bored with the rigid academic environment and decided to pursue his own educational curiosity and learn about his environment according to his interpretation of what is important to know. This bivariate analysis did not have the correct data to measure and analyze for environmental variables.

2.

Management of a regional bus line wanted to measure the correlation between two variables. The dependant variable is the passenger/mile ratio and the independent variable is the cost of gas. Therefore, y is the dependant variable and x is the independent variable.

The correlation coefficients for the price to mile and passenger ratio is varied. The null hypothesis is H0 with N=5 and RHO=0 with the year price and mile information given as the following

Statistical Techniques in Business & Economics

The data is spread out but is almost perfectly correlated, suggesting there is a strong and positive, linear correlation between the cost of gas and the passenger/mile ratio. Therefore the null hypothesis or H=0 is accepted.

3. A correlation matrix for a company measures the sales force activity as a function of a number of variables including age, years of service, and current sales. The matrix is depicted below:

The results of the correlation are interesting. Age and Years of Service result with the greatest correlation as dependant and independent variables. The correlation is .64 and suggests that age is a function in the years of service. Therefore, the older an employee becomes, the more service in years will accrue. However, this is to an extent. If one were to assume a ten-year career, on average, the statistic suggests an average of 6.5 years on the job. Therefore, it is not a perfect measure of years on the job but gives an indication that independent of the age of the employee, they will have about a 7-year career.

The strength is not as great as in the previous data however the relative strength of the correlation between years of service and current sales is close to .5 and therefore suggests that beyond a certain number of years of experience, sales seems to increase as a greater percentage of each additional year of experience.

Hence, a greater marginal increase is expected after x number of years of service. This may likely be due to a reputation established in the neighborhood after working in the community for a number of years or having sold a number of cars and the word of mouth effect enabling greater sales as a function of years.

Age to Current Sales is very interesting as it is negatively and weakly correlated. This suggests that as Age increases, Current Sales decreases but the correlation between the increase in age and the decrease in current sales is not strong enough to suggest that age is a determining function in the outcome of current sales. Therefore, age does not effect the current sales number as any employee on staff with age as a non-factor is able to lead in the current sales figures.

4. The following is a regression model depicting the likelihood of buying a new car given total family income and the likelihood of buying tickets to a rock concert given age.

a.) Y^ = a^ + ss^X; Y^ = 3.5 + .7X, where Y^ = likelihood of buying a new car and X = total family income

b) Y^= a^ + ss^X; Y^= 3.5 - .4x, where Y^ = the likelihood of buying tickets to a rock concert and X = age.

The regression equation for a is a predictor of Y^ pronounced Y-hat suggests that for every unit increase in x, or family income, y increases by 4.2. So for every increase in total family income the likelihood of buying a new car increases by 4.2.

The regression equation for b is a predictor of Y^ and suggests that for every unit increase in x, or age, y increases by 3.9. For every unit increase in age, the likelihood of buying tickets to a rock concert increases by 3.9.

The ANOVA summary table is the result of a regression of sales on year of sales

Explained by regression 605, 370, 750 1-3.12 with the sum of squares, degrees of freedom, mean, and f-value shown respectively. Unexplained by the regression is 1,551,381,712 8 193,922, 714 and the total error is 9. The alpha value to test whether the relationship is statistically significant is alpha=.05 or 5% so the test is for 95% confidence or that the distribution is within 2?. Yes the test is significant at alpha .05 and does not need to test at alpha .01 however if one does not feel .05 is sufficient then testing at 3? is the next step.

6. A metropolitan economist attempts to predict the average total budget for retired couples in Phoenix based on the average of U.S. urban retired couples total budget. An r squared value of .7824 is the result of the analysis. This is to say that 78% of the data is explained by the dependant variable, or that 78% of the result is explained by the choice in dependant variable. A value above .8 would be a nice target but .78 is very close and therefore suggests that much of the data has been explained by using the mean of U.S. urban retired couples. The result would suggest that perhaps Phoenix may have to lower the predicted average of total budget required as the unexplained 21 and a fraction may imply a higher than necessary budget figure.