A Survey Conducted by a Research Team Was to Investigate

question 63

Essay

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 employees is selected and the data is given below. $\begin{array}{|c|c|c|c|}\hline\begin{array}{c}\text { Education (No. of } \\\text { years) }\end{array} & \begin{array}{c}\text { Length of tenure in } \\\text { current employment } \\\text { (No. of years) }\end{array} & \text { Age (No. of years) } & \text { Annual income (\$) } \\\hline 17 & 8 & 40 & 124,000 \\\hline 12 & 12 & 41 & 30,000 \\\hline 20 & 9 & 44 & 193,000 \\\hline 14 & 4 & 42 & 88,000 \\\hline 12 & 1 & 19 & 27,000 \\\hline 14 & 9 & 28 & 43,000 \\\hline 12 & 8 & 43 & 96,000 \\\hline 18 & 10 & 37 & 110,000 \\\hline 16 & 12 & 36 & 88,000 \\\hline 11 & 7 & 39 & 36,000 \\\hline 16 & 14 & 36 & 81,000 \\\hline 12 & 4 & 22 & 38,000 \\\hline 16 & 17 & 45 & 140,000 \\\hline 13 & 7 & 42 & 11,000 \\\hline 11 & 6 & 18 & 21,000 \\\hline 20 & 4 & 40 & 151,000 \\\hline 19 & 7 & 35 & 124,000 \\\hline 16 & 12 & 38 & 48,000 \\\hline 12 & 2 & 19 & 26,000 \\\hline 10 & 6 &44& 124,000 \\\hline\end{array}$
a. Check if the F test leads to conclude that an overall regression relationship exists. If yes, use the t test to
determine the significance of each independent variable. What is the conclusion for each test at the 0.05 level of significance?
b. Remove all independent variables that are not significant at the 0.05 level of significance from the estimated
regression equation. What is your estimated regression equation in this case?

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Definitions:

Nephron

The basic structural and functional unit of the kidney, responsible for filtering blood and producing urine.

Glomerular Capsule

A cup-shaped structure surrounding the glomerulus in each nephron of the kidney, where filtration of blood plasma occurs.

Afferent Arteriole

A small artery that leads into the glomerulus of the kidney, where it divides into capillaries for blood filtration.

Efferent Arteriole

A small blood vessel that carries blood away from the glomeruli of the kidney.