RATED A+ 2025/2026
The residuals from a linear regression model can be used to check the underlying assumptions
and to investigate model adequacy.
True
The standard method for estimating the parameters in a simple linear regression model is the
method of least squares
true
A fitted linear regression model is yhat=10+2x. If x = 1 and the corresponding observed value
of y = 11, the residual at this observation is:
yi-yhat ->(11-(10+2*1))=-1
If both the response and regressor variables are random variables, we can calculate a
correlation coefficient that reflects the linear relationship between these two variables.
True
The correlation coefficient and the slope provide equivalent information in simple linear
regression.
false (also need B0)
Which of the following is not true?
If S is the sample space, then the P(S) = 0
Probabilities are numbers in the [0,1] interval.
A continuous random variable is one with an interval of real numbers for its range.
A discrete sample space can be made up of a finite set of outcomes.
All of these options are not true.
If S is the sample space, then the P(S) = 0
The set of all possible outcomes of a random experiment is called the sample space and is
denoted by the letter 𝑆.
Events are said to be independent when the occurrence of one event does not affect the
probability of another.
, true
A random variable is a function that assigns a probability to each outcome in the sample space
of a random experiment.
false
A random variable is a function that assigns a real number to each outcome in the sample space
of a random experiment.
If two events are independent of one another then the probability of their intersection is zero.
FALSE - mutually exclusive has intersection of zero
An experiment that results in the same outcome when replicated is referred to as a random
experiment.
False
A random variable is said to be discrete if it has an infinite number of values in a finite interval
of its range.
False
A discrete random variable is one with a finite or countably infinite range. Its values are
obtained by counting.
A continuous random variable is one with an interval (either finite or infinite) of real numbers
for its range. Its values are obtained by measuring.
Discrete random variables:
-Number of scratches on a surface.
-Proportion of defective parts among 100 tested.
-Number of transmitted bits received in error.
-Number of common stock shares traded per day.
Continuous random variables:
Continuous random variables:
-Electrical current and voltage.
-Physical measurements, e.g., length, weight, time, temperature, pressure.
All the fourth-graders in a certain elementary school took a standardized test. A total of 71% of
the students were found to be proficient in reading, 72% were found to be proficient in