Asked by Fahad Hashmi on Jul 18, 2024
Verified
The data referred to in this question were collected on 41 employees of a large company.The company is trying to predict the current salary of its employees from their starting salary (both expressed in thousands of dollars) .The SPSS regression output is given below as well as some summary measures: John Doe works for this company.He started with a salary of $15,300.Predict his current salary with a 90% confidence interval.Express the interval in the appropriate units.
A) ($15,683;$45,537)
B) ($18,204;$43,015)
C) ($28,580;$32,640)
D) ($31,516;$32,885)
Confidence Interval
A collection of numbers, derived from collecting sample information, which is assumed to contain the value of an unidentified population aspect.
Current Salary
The present monetary compensation someone receives from employment, before taxes and deductions.
Starting Salary
The amount of money that a new employee is paid at the beginning of their employment.
- Determine and explain the confidence intervals relevant to linear regression coefficients.
- Comprehend the principle of prediction intervals as it pertains to regression analysis.
Verified Answer
predicted salary = 5.152 + 1.657(starting salary)
Substituting the given values for John Doe:
predicted salary = 5.152 + 1.657(15.3) = $30,050.61
To find the 90% confidence interval, we need to use the formula:
predicted salary ± (critical value)(standard error)
From the output, the standard error is 4.827 and the critical value for a 90% confidence interval with 39 degrees of freedom is 1.684.
Substituting these values:
interval = $30,050.61 ± (1.684)(4.827) = ($18,203.77, $43,897.45)
So the answer is B: ($18,204;$43,015)
Learning Objectives
- Determine and explain the confidence intervals relevant to linear regression coefficients.
- Comprehend the principle of prediction intervals as it pertains to regression analysis.
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