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SRM ExamDetermine which of the following statements is/are true.
1. The leverage for each observation in a linear model must be between 1n1n and 1.
2. The nn leverages in a linear model must sum to the number of explanatory variables.
3. If an explanatory variable is uncorrelated with all other explanatory variables, the corresponding
variance inflation factor would be zero. - correct answer ✔✔1. The leverage for each observation in a
linear model must be between 1n1n and 1.
2. FALSE. The leverages must sum to p+1p+1, which is the number of predictors plus the intercept.
3. FALSE. If an explanatory variable is uncorrelated with all other explanatory variables, the
corresponding variance inflation factor would be 1.
How do you calculate the bias of the slope estimator when ordinary least squares regression is used. -
correct answer ✔✔0 - ordinary least squares is unbias
Which matrix's diagonal elements are the leverages - correct answer ✔✔the hat matrix:
X(XTX)−1XTX(XTX)−1XT
An analyst is modeling the probability of a certain phenomenon occurring. The analyst has observed that
the simple linear model currently in use results in predicted values less than zero and greater than one.
what model should they use to address this issue - correct answer ✔✔Use a logit function to transform
the linear model into only predicting values between 0 and 1.
Determine which of the following statements is/are true about autoregressive models of order one,
AR(1).
1. An AR(1) model is a meandering process.
2. A stationary AR(1) model is a generalization of both a white noise process and a random walk model.
, 3. The lag kk autocorrelation of a stationary AR(1) model is always non-negative. - correct answer
✔✔None:
I is false. Not all AR(1) model is a meandering process. An AR(1) model with −1<β1<0−1<β1<0 is not a
meandering process. An AR(1) model with 0<β1<10<β1<1 is a meandering process.
II is false. A general AR(1) model is a generalization of a white noise process and a random walk model.
However, note that the slope coefficient of a stationary AR(1) model is restricted to be between -1 and 1
exclusively, i.e. −1<β1<1−1<β1<1. This means that a stationary AR(1) model is not a generalization of a
random walk model since β1=1β1=1 for a random walk model.
III is false. This is only true if the slope coefficient is non-negative, i.e. β1≥0β1≥0. If it is negative, then the
lag kk autocorrelation will be negative when kk is odd. Recall that a stationary AR(1) model has a lag kk
autocorrelation of ρk=βk1ρk=β1k.
Determine which of the statements is/are true about smoothing with moving averages where kk is the
smoothing parameter.
1. k=1k=1 results in no smoothing.
2. It is risky to choose a small value for kk because we may lose sight of the real trends due to over-
smoothing.
3. When smoothing with moving averages is used for forecasting, the model is called a globally constant
mean model. - correct answer ✔✔1 only
I is true. Using k=1k=1 results in no smoothing. The larger the kk, the smoother the estimate.
II is false. A small kk doesn't cause oversmoothing. It is risky to choose a large value for kk because we
may oversmooth the data and lose sight of the real trends.
III is false. Smoothing with moving averages results in a locally constant mean model. The model is only
called a globally constant mean model when equal weight is given to all observations.
Determine which of the following statements is/are true for a simple linear relationship,
y=β0+β1x+εy=β0+β1x+ε.
1. If ε=0ε=0, the 95% confidence interval is equal to the 95% prediction interval.
2. The prediction interval is always at least as wide as the confidence interval.
3. The prediction interval quantifies the possible range for E(y∣x)E(y∣x) - correct answer ✔✔1 and 2
1. True. The prediction interval accounts for the irreducible error. If the irreducible error is zero, the
prediction interval will be the same as the confidence interval.
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