ISYE 6414 COMPREHENSIVE CORRECT QUESTIONS
AND ANSWERS SURE A+
✔✔sample variance estimator (s^2) - ✔✔the estimator of the variance of the error terms
(is chi-square with n - 1 degrees of freedom)
✔✔positive value for ß1 - ✔✔a direct relationship
between the predicting variable x and the response variable y
✔✔negative value of ß1 - ✔✔an inverse relationship between x and y.
✔✔ß1 is close to zero. - ✔✔there is not a significant association between the predicting
variable x, and the response variable y.
✔✔ß1 hat - ✔✔is the estimated expected change in the response variable associated
with
one unit of change in the predicting variable.
✔✔ß0 hat - ✔✔is the estimated expected value of the response variable, when the
predicting variable equals zero
✔✔we use ß1 hat - ✔✔when we interpret whether the relationship between x and y is
positive, negative, or
there is no relationship.
✔✔when we make statistical statements
about the relationship - ✔✔we always have to mention the statistical significance,
whether
statistically significantly positive, statistically significantly negative, or no statistical
significance.
,✔✔estimated standard deviation - ✔✔in model summary, look for Residual standard
error
✔✔estimate of the variance (from output) - ✔✔we need to take the square of the
residual standard error
✔✔extrapolation - ✔✔not within the range of the observed axis, predicting larger than
the values observed
✔✔expectation of a linear combination of random
variables - ✔✔is equal to the linear combination of the expectations.
✔✔expectation of the estimator for the slope parameter is - ✔✔exactly ß1. ( ß1
( ß1 hat is an unbiased estimator for ß1)
✔✔unbiasedness - ✔✔the fact that the expectation of the estimator is exactly the true
parameter that we're estimating
✔✔sampling distribution of ß1 hat - ✔✔is a T distribution with N - 2 degrees of freedom.
✔✔to obtain a confidence interval with (1-alpha)% confidence level - ✔✔we can center
the confidence interval at the estimated value for β1, plus or minus the (1-alpha critical
point T.
✔✔T value - ✔✔the estimated value for ß1 /the standard error of the
estimator.
✔✔If that T value is large - ✔✔reject the null hypothesis that ß1 is equal to zero. If
the null hypothesis is rejected, we interpret this that ß1 is statistically significant.
✔✔Statistical significance means - ✔✔that ß1 is statistically different from zero.
✔✔If the T value is larger
than its critical point in absolute value, - ✔✔we say that the slope coefficient is
statistically
significantly different from c.
✔✔If the P
value is small, for example, smaller than .01, - ✔✔we would reject the new hypothesis.
✔✔For ß1 greater than zero - ✔✔we're interested on the right tail of the distribution of
the
ß1 hat.
, ✔✔For ß1 smaller than zero - ✔✔we're interested on the left tail.
✔✔sample distribution of ß0 - ✔✔is also T distribution
✔✔To perform statistical inference, we need to find: - ✔✔● the estimated coefficient β1
and its variance along with the sample distribution of β1.
● the estimated coefficient for the intercept β0 and its variance along with the sample
distribution
● whether the coefficient β1 is statistically significant.
● whether β1 is statistically positive.
✔✔the estimated variance (of ß1) - ✔✔we need to take the square of the standard
error
✔✔function pt() - ✔✔stands for the probability
of a t-distribution, gives left tail evaluating the quantile equal to the t-value. In order to
get the right tail of
that distribution we'd have to take one
minus that probability.
✔✔P-value - ✔✔is a measure of how rejectable the null hypothesis
is. The smaller the p-value is, the more rejectable the null hypothesis is for the
observed data, given the observed data. It's not the probability of rejecting the null
hypothesis, nor is it the probability that the null hypothesis is true.
✔✔x* under estimation - ✔✔it's really an average across all possible settings when we
could observe x*.
✔✔x* under prediction - ✔✔x* is considered an observation under a new setting, we
focus on one particular setting.
✔✔normal - ✔✔Y-hat has a ___ distribution. Thus, regression line is an unbiased
estimator just like the estimators of the regression
coefficients.
✔✔x* equals - ✔✔x hat. variance is going to be smaller at the center of the average and
is
going to increase as we go away from the average
✔✔as the predicted
value x* is away from the average. - ✔✔The uncertainty in the estimated regression line
is going to be higher
AND ANSWERS SURE A+
✔✔sample variance estimator (s^2) - ✔✔the estimator of the variance of the error terms
(is chi-square with n - 1 degrees of freedom)
✔✔positive value for ß1 - ✔✔a direct relationship
between the predicting variable x and the response variable y
✔✔negative value of ß1 - ✔✔an inverse relationship between x and y.
✔✔ß1 is close to zero. - ✔✔there is not a significant association between the predicting
variable x, and the response variable y.
✔✔ß1 hat - ✔✔is the estimated expected change in the response variable associated
with
one unit of change in the predicting variable.
✔✔ß0 hat - ✔✔is the estimated expected value of the response variable, when the
predicting variable equals zero
✔✔we use ß1 hat - ✔✔when we interpret whether the relationship between x and y is
positive, negative, or
there is no relationship.
✔✔when we make statistical statements
about the relationship - ✔✔we always have to mention the statistical significance,
whether
statistically significantly positive, statistically significantly negative, or no statistical
significance.
,✔✔estimated standard deviation - ✔✔in model summary, look for Residual standard
error
✔✔estimate of the variance (from output) - ✔✔we need to take the square of the
residual standard error
✔✔extrapolation - ✔✔not within the range of the observed axis, predicting larger than
the values observed
✔✔expectation of a linear combination of random
variables - ✔✔is equal to the linear combination of the expectations.
✔✔expectation of the estimator for the slope parameter is - ✔✔exactly ß1. ( ß1
( ß1 hat is an unbiased estimator for ß1)
✔✔unbiasedness - ✔✔the fact that the expectation of the estimator is exactly the true
parameter that we're estimating
✔✔sampling distribution of ß1 hat - ✔✔is a T distribution with N - 2 degrees of freedom.
✔✔to obtain a confidence interval with (1-alpha)% confidence level - ✔✔we can center
the confidence interval at the estimated value for β1, plus or minus the (1-alpha critical
point T.
✔✔T value - ✔✔the estimated value for ß1 /the standard error of the
estimator.
✔✔If that T value is large - ✔✔reject the null hypothesis that ß1 is equal to zero. If
the null hypothesis is rejected, we interpret this that ß1 is statistically significant.
✔✔Statistical significance means - ✔✔that ß1 is statistically different from zero.
✔✔If the T value is larger
than its critical point in absolute value, - ✔✔we say that the slope coefficient is
statistically
significantly different from c.
✔✔If the P
value is small, for example, smaller than .01, - ✔✔we would reject the new hypothesis.
✔✔For ß1 greater than zero - ✔✔we're interested on the right tail of the distribution of
the
ß1 hat.
, ✔✔For ß1 smaller than zero - ✔✔we're interested on the left tail.
✔✔sample distribution of ß0 - ✔✔is also T distribution
✔✔To perform statistical inference, we need to find: - ✔✔● the estimated coefficient β1
and its variance along with the sample distribution of β1.
● the estimated coefficient for the intercept β0 and its variance along with the sample
distribution
● whether the coefficient β1 is statistically significant.
● whether β1 is statistically positive.
✔✔the estimated variance (of ß1) - ✔✔we need to take the square of the standard
error
✔✔function pt() - ✔✔stands for the probability
of a t-distribution, gives left tail evaluating the quantile equal to the t-value. In order to
get the right tail of
that distribution we'd have to take one
minus that probability.
✔✔P-value - ✔✔is a measure of how rejectable the null hypothesis
is. The smaller the p-value is, the more rejectable the null hypothesis is for the
observed data, given the observed data. It's not the probability of rejecting the null
hypothesis, nor is it the probability that the null hypothesis is true.
✔✔x* under estimation - ✔✔it's really an average across all possible settings when we
could observe x*.
✔✔x* under prediction - ✔✔x* is considered an observation under a new setting, we
focus on one particular setting.
✔✔normal - ✔✔Y-hat has a ___ distribution. Thus, regression line is an unbiased
estimator just like the estimators of the regression
coefficients.
✔✔x* equals - ✔✔x hat. variance is going to be smaller at the center of the average and
is
going to increase as we go away from the average
✔✔as the predicted
value x* is away from the average. - ✔✔The uncertainty in the estimated regression line
is going to be higher
