IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
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 statistic for testing the slope is zero?
With r = -0.6, R² is 0.36. F equals R² times (n-2) divided by (1-R²), which is 0.36 × 18 / 0.64 = 10.125, about 10.1. The sign of r does not matter for F.
- A5.63
- B9.0
- C10.1Correct
- D12.0
- 0.5625
Explanation
R² = 0.36. F = R²(n-2)/(1-R²) = 0.36×18/0.64 = 10.125, about 10.1. Ignoring the negative sign is correct as R² is positive; using n instead of n-2 gives 11.25, which is wrong.
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
- In a multiple linear regression with p parameters (including the intercept) fitted to n observations, H is the hat matrix X(XᵀX)⁻¹Xᵀ. Which …
- In a simple linear regression with n = 27 observations, the total sum of squares is 500 and the regression sum of squares is 300. What is th…
- 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 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…
- 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…