IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
A simple linear regression of y on x is fitted by least squares to n = 20 observations. The summary statistics are Sxx = 50, Sxy = 120 and Syy = 330, where Sxx = Σ(x − x̄)², and so on. What is the least squares estimate of the slope?
The least squares slope equals Sxy divided by Sxx, which is 120 divided by 50, giving 2.40. Syy is not needed for the slope estimate. Inverting the ratio or using Syy gives incorrect values.
- A0.417
- B2.40Correct
- C2.75
- D6.60
- 0.364
Explanation
The slope estimate is Sxy/Sxx = 120/50 = 2.40. Option 0.417 is Sxx/Sxy, which inverts the ratio. Option 2.75 is Sxy/Sxx taken with the wrong sums, and 6.60 is Syy/Sxx.
Did you get it right without looking?
One question tells you little. A timed set on Linear regression models shows your real accuracy, how long you take and where you lose marks.
More Linear regression models questions
- Data (x, y): (1, 3), (2, 5), (3, 7), (4, 9) are fitted by least squares as y = a + bx. What is the residual sum of squares?
- In simple linear regression of Y on X with 20 observations, the sample correlation between X and Y is r = -0.6. What is the value of the F s…
- In a multiple regression with p = 4 parameters (including intercept) and n = 20 observations, one observation has standardised residual r = …
- In the multiple linear regression model Y = Xβ + ε, where X is an n × p design matrix of full column rank (including a column of ones) and t…
- In a simple linear regression fitted to 12 observations, the total sum of squares is 500 and the residual sum of squares is 125. What is the…
- A regression with an intercept and 3 explanatory variables is fitted to n = 24 observations. The total sum of squares is 480 and the residua…