Use the Manufacturing database from "Excel Databases.xls" on Blackboard. Use Excel to develop a multiple regression model to pre
dict Cost of Materials by Number of Employees, Number of Production Workers, Value Added by Manufacture, New Capital Expenditures, and End-of-Year Inventories. Use Excel to perform a backward elimination regression analysis at a 5% level of significance. What is the test statistic of the independent variable that is dropped from the linear model in the first step. Write your answer as a number and round to 2 decimal places.
1 answer:
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Answer:
The 95% confidence interval would be given by (2.351;3.525)
Explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
2) Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (2.351;3.525)