Quantitative Methods
In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The multiple coefficient of determination is
.65.
In regression analysis, the error term ε is a random variable with a mean or expected value of
0
A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have
130 degrees of freedom.
In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is
14.8
In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is
14.8.
A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have
181 degrees of freedom.
In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. y ^ = 29 + 18x1 + 43x2 + 87x3 For this model, SSR = 600 and SSE = 400. MSR for this model is
200.
In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
3 and 43.
An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 25 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are
3 and 96.
An ANOVA procedure is used for data that was obtained from five sample groups each comprised of six observations. The degrees of freedom for the critical value of F are
4 and 25.
In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is
40
An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The critical value of F occurs with
5 numerator and 114 denominator degrees of freedom
We use non-parametric ANOVA instead of parametric ANOVA if
All of the above
In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?
F test
The F ratio in a completely randomized ANOVA is given by
MSTR/MSE.
Non-parametric ANOVA test on:
Median
What is the assumption not required for non-parametric ANOVA?
Population are not normally distributed
Which of the following is not a required assumption for the analysis of variance?
Populations under consideration have equal means.
In an analysis of variance where the total sample size for the experiment is and the number of populations is k, the mean square due to error is
SSE/(n T - k).
In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square due to error is
SSE/(n T - k).
The correct relationship between SST, SSR, and SSE is given by
SSR = SST - SSE.
Which of the following is correct?
SST = SSR + SSE
When an analysis of variance is performed on samples drawn from k populations, the mean square due to treatments (MSTR) is
SSTR/(k - 1).
In regression analysis, which of the following assumptions is not true about the error term ε?
The expected value of the error term is one.
A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical independent variables in a regression model is called
a dummy variable.
The mathematical equation which has the form of E(y) = β0 + β1x 1+ β2x 2+ ... + βpx prelating the expected value of the dependent variable to the value of the independent variables is
a multiple regression equation.
The equation which has the form of E(y) = y ^= b0 + b1 x 1+ b2 x 2+ ... + bp x pis
an estimated multiple regression equation.
The process of using the same or similar experimental units for all treatments is called
blocking.
The coefficient of determination
cannot be negative.
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the
coefficient of determination.
An experimental design where the experimental units are randomly assigned to the treatments is known as _____ design.
completely randomized design.
In regression analysis, the response variable is the
dependent variable.
In regression analysis, the variable that is being predicted is the
dependent variable.
In the ANOVA, treatments refer to
different levels of a factor.
In an ANOVA procedure, a term that means the same as the term "variable" is
factor
An experimental design that permits simultaneous statistical conclusions about two or more factors is a
factorial design.
A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: y ^= 7 - 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The coefficient of x2 indicates that if television advertisement is increased by $1 (holding the unit price constant), sales are expected to
increase by $5000.
A multiple regression model has the estimated form y ^= 7 + 2x1 + 9x2 As x1 increases by 1 unit (holding x2 constant), y is expected to
increase by 2 units.
A multiple regression model has the estimated form y ^= 5 + 6x + 7w As x increases by 1 unit (holding w constant), y is expected to
increase by 6 units.
A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: y ^= 7 - 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The coefficient of the unit price indicates that if the unit price is
increased by $1 (holding advertisement constant), sales are expected to decrease by $3000.
In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as
interaction.
The mean square is the sum of squares divided by
its corresponding degrees of freedom.
In testing for the equality of k population means, the number of treatments is
k
If a categorical variable has k levels, the number of dummy variables required is
k - 1.
Larger values of R 2 imply that the observations are more closely grouped about the
least squares line.
A term used to describe the case when the independent variables in a multiple regression model are correlated is
multicollinearity.
The adjusted multiple coefficient of determination is adjusted for the
number of independent variables.
Regression analysis is a statistical procedure for developing a mathematical equation that describes how
one dependent and one or more independent variables are related.
In an analysis of variance, one estimate of σ2 is based upon the differences between the treatment means and the
overall sample mean.
The required condition for using an ANOVA procedure on data from several populations is that the
sampled populations have equal variances.
If we are testing for the equality of three population means, we should use the
test statistic F.
The ratio of MSR to MSE yields
the F statistic.
In the analysis of variance procedure (ANOVA), "factor" refers to
the independent variable.
In a regression model, the variance of the error term ε is assumed to be
the same for all values of the independent variable.
The ANOVA procedure is a statistical approach for determining whether or not the means of
three or more populations are equal.
In regression analysis, the independent variable is
used to predict the dependent variable.
In ANOVA, which of the following is not affected by whether or not the population means are equal?
within-treatments estimate of σ 2
In a factorial experiment, if there are x levels of factor A and y levels of factor B, there is a total of
xy treatment combinations.
In a regression model, the error term ε is assumed to be a random variable with a mean of
zero.
