Asked by Alejandra Veloz on May 16, 2024
Verified
In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations: . The least squares estimates of the slope and y-intercept are respectively:
A) 1.5 and 0.5
B) 2.5 and 1.5
C) 1.5 and 2.5
D) 2.5 and -5.0
E) none of these
Least Squares Estimates
A statistical method used to determine the line of best fit by minimizing the sum of squares of the errors between observed and predicted values.
Slope
In mathematics and statistics, it represents the rate at which a line inclines or declines, showing the change in the dependent variable for a unit change in the independent variable.
Y-Intercept
The location at which a line or curve crosses the y-axis in a coordinate system.
- Discern the functional role of the slope and intercept in regression equations.
Verified Answer
slope = (nΣ(XY) - ΣXΣY) / (nΣ(X^2) - (ΣX)^2)
y-intercept = (ΣY - slopeΣX) / n
Plugging in the values from the sample, we get:
slope = (10(155) - (65)(33)) / (10(81.4) - (65)^2) = 2.5
y-intercept = (33 - (2.5)(65)) / 10 = -5
Therefore, the least squares estimates of the slope and y-intercept are 2.5 and -5, respectively, which corresponds to answer choice D.
Learning Objectives
- Discern the functional role of the slope and intercept in regression equations.
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