Let us use the following data to see whether higher-paid CEO’s control bigger co
ID: 3253855 • Letter: L
Question
Let us use the following data to see whether higher-paid CEO’s control bigger companies.
x salary($ millions)
0.8
1.0
1.1
1.7
2.3
y revenue($billions)
14
11
19
20
25
1.) If a CEO has an annual salary of $1.5 million, what is his or her annual company revenue as predicted by the least-squares line?
2.) Find a 90% confidence interval for your prediction of problem 1.
please show steps by step, or show how to do on TI-84 calc, thank you!
x salary($ millions)
0.8
1.0
1.1
1.7
2.3
y revenue($billions)
14
11
19
20
25
Explanation / Answer
Solution:-
Formula:
Y = a + bX
where
b = r (SDy / SDx)
and a = Ybar - bXbar
Where,
Y = LSRL Equation
b = The slope of the regression line
a = The intercept point of the regression line and the y axis.
X = Mean of x values
Y = Mean of y values
SDx = Standard Deviation of x
SDy = Standard Deviation of y
r = (Nxy - xy) / sqrt ((Nx2 - (x)2) x (Ny)2 - (y)2)
Least Square Regression Line Equation Y
7.812x + 7.02
where slope is 7.812 and Y-intercept is 7.02.
1.) If a CEO has an annual salary of $1.5 million, what is his or her annual company revenue as predicted by the least-squares line?
Using the
Least Square Regression Line Equation Y = 7.812x + 7.02
given x = $1.5 million
Y = 7.812 * 1.5 + 7.02
= 18.738
His/her annual company revenue as predicted by the least-squares line is $ 18.738 billions.
(b) Find a 90% confidence interval for your prediction of problem 1.
Formula Used:
0 + t ((1-a)/2, n-k-1) SE0
Where, 0 = Regression intercept
k = Number of Predictors
n = Sample Size
SE0 = Standard Error
= Percentage of Confidence Interval
t = t-Value
Confidence interval, 90% = 90/100 = 0.90
-15.30499 0 29.34499
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