QBA unit 2 quiz questions exam study guide
Regression analysis was applied between sales (y in $1000) and advertising (x in $100) and the following estimated regression equation was obtained. = 80 + 6.2x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is
$700,000. Estimated sales = 1000 × (80 + 6.2 × 10000/100) = $700,000
Regression analysis was applied, and the least squares regression line was found to be y^= 500 + 4x What would the residual be for an observed value of (3, 510)?
-2 Predicted = 500 + 4 × 3 = 512. Residual = Observed - Predicted = 510 - 512 = -2
In regression analysis, the error term ε is a random variable with a mean or expected value of
0
In a regression analysis, if SSE = 600 and SSR = 300, then the coefficient of determination is
0.333 r2 = SSR / SST = 300 / 900 = 0.333
For a multiple regression model, SST = 200 and SSE = 60. The multiple coefficient of determination is
0.70. Multiple coefficient of determination = SSR / SST = (200 - 60) / 200 = 0.70.
In a regression analysis, if SST = 4500 and SSR = 2925, then the correlation coefficient could be
0.806 or -0.806 r2 = SSR / SST = (2925 / 4500) = 0.65 Correlation r = √(0.65) = 0.806 or -0.806 depending on the Slope
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
If the coefficient of correlation is .4, the percentage of variation in the dependent variable explained by the variation in the independent variable is
16%. Coefficient of determination = (0.4)2 = 16%
Part of an ANOVA table is shown below. Source ofVariation Sum ofSquares Degreesof Freedom MeanSquare F Between Treatments 64 8 Within Treatments (Error) 2 Total 100 The number of degrees of freedom corresponding to within-treatments is
18
For a Simple Linear Regression Model of Sample size 75, SSR was 345 and SSE was 1355. What would be the F statistics for this model?
18.5867 Residual df = n - k - 1 = 75 - 1 - 1 = 73 k = 1 as there is only 1 independent variable MSR = SSR / 1 = 345 / 1 = 345. MSE = SSE / 73 = 1355 / 73 = 18.5616. F = MSR / MSE = 345 / 18.5616 = 18.5867
The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). = 30 + 0.7x1 + 3x2 Also provided are SST = 1200 and SSE = 384. The test statistic for testing the significance of the model is
28.69 Degrees of freedom for SSR is 2 and for SSE is 30 - 2 - 1 = 27. Thus, MSR = (1200 - 384) / 2 = 408, and MSE = 384 / 27 = 6. Thus, F-statistics = 408 / 14.2222 = 28.687.
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 k = 5, nT = 5(6) = 30, df numerator = k - 1 = 5 - 1 = 4, df denominator = nT - k = 30 - 5 = 25.
In a multiple regression model involving 60 observations, the following estimated regression equation was obtained: = 30 + 18x1 + 43x2 + 87x3+ 90x4 For this model, SSR = 800 and SST = 1400. The numerator and denominator degrees of freedom (respectively) for the F critical value would be
4, 55 Numerator degrees of freedom = 4 since there are four independent variables. Denominator degrees of freedom = n - k - 1 = 60 - 4 - 1 = 55. k = number of independent columns. Answer: (4, 55)
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information. SSTR = 300 (Sum of Squares Due to Treatments)SST = 800 (Total Sum of Squares) The number of degrees of freedom corresponding to within-treatments is
60
Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8x Based on the above estimated regression equation, if advertising is $3000, then the point estimate for sales (in dollars) is
66,000 1000 × (12 + 1.8 × 3000/100) = $66,000
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information. SSTR = 300 (Sum of Squares Due to Treatments)SST = 800 (Total Sum of Squares) The mean square due to treatments (MSTR) is
75
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information. SSTR = 300 (Sum of Squares Due to Treatments)SST = 800 (Total Sum of Squares) The mean square due to error (MSE) is
8.33
Given the following information, what is the correlation coefficient? SSE = 420.4, SST = 1028.8
Coeff of Determination = SSR / SST = (1028.8 - 420.4) / 1028.8 = 0.5914 Correlation r = √0.5914 = 0.7690 because slope is positive
In a regression analysis, if SST = 500 and SSE = 200, then the coefficient of determination is
Coefficient of Determination = SSR / SST = (500 - 200) / 500 = 0.60
In a regression analysis, the coefficient of correlation is 0.15. The coefficient of determination in this situation is
Coefficient of determination = (0.15)2 = 0.0225
In a Linear Regression Model, the correlation coefficient was calculated to be -0.8660 and the SSE was 160. What would be SST for this Model?
Coefficient of determination r2 = SSR / SST SST = SSR + SSE = SSR + 160 Thus, SSR / (SSR + 160) = (-0.866)2 = 0.75; SSR = 0.75 × 160 / (1 - 0.75) = 480; SST = 480 + 160 = 640
An experimental design where the experimental units are randomly assigned to the treatments is known as _____ design.
Completely Randomized
The following information regarding a dependent variable (y) and an independent variable (x) is provided. SSE = 1.9 SST = 6.8 The MSE is
MSE = SSE / (n - k - 1) = 1.9 / 3 k = 1 as there is only one independent variable
Consider the following information. SSTR = 6750 H0: μ1 = μ2 = μ3 = μ4 = μ5 SSE = 8000 Ha: At least one mean is different If n = 5, the mean square due to error (MSE) equals
MSE=SSE/nT-k 8000/25-5 =400
In a multiple regression model involving 44 observations, the following estimated regression equation was obtained: For this model, SSR = 800 and SST = 1400. The multiple coefficient of determination for the above model is
Multiple coefficient of determination = SSR / SST = 800 / 1400 = 0.571.
In a multiple regression analysis, SSR = 1000 and SSE = 200. The F statistic for this model is
Not enough information is provided to answer this question. The number of independent variables or p is not given
If the coefficient of correlation is 0.7, the percentage of variation in the dependent variable explained by the variation in the independent variable is
R2 = 0.72 = 49%
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/(nT - k).
In an analysis of variance problem if SST = 120 and SSTR = 90, then SSE is
SSE=SST-SSTR 120-90= 30
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information. SSTR = 300 (Sum of Squares Due to Treatments)SST = 800 (Total Sum of Squares) The sum of squares due to error (SSE) is
SSE=SST-SSTR 800-300=500
In a regression and correlation analysis, if r2 = 1, then
SSR = SST.
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 the regression analysis equation the model in the form of the equation, The X represents
The independent variable
A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). Σx = 90Σ(y - )(x - ) = 466Σy = 170Σ(x - )2 = 234n = 10Σ(y - )2 = 1434SSE = 505.98 The sum of squares due to regression (SSR) is
The sum of squares due to regression (SSR) is
The process of using the same or similar experimental units for all treatments is called
blocking
The coefficient of determination
cannot be negative.
The interval estimate of the mean value of y for a given value of x is the
confidence interval estimate.
A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: = 9 - 4x The above equation implies that if the price is increased by $1, the demand is expected to
decrease by 4000 units. Decrease by 4 × 1 × 1000 because the slope is negative
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
The independent variable of interest in an ANOVA procedure is called a
factor
An experimental design that permits simultaneous statistical conclusions about two or more factors is a
factorial design
In a multiple regression model, the values of the error term ε are assumed to be
independent of each other
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
In a regression analysis, the standard error of the estimate is determined to be 4. In this situation, the MSE
is 16 MSE = (Standard Error)2 = 42
The mean square is the sum of squares divided by
its corresponding degrees of freedom.
It is possible for the coefficient of determination to be
less than 1.
A multiple regression model has
more than one independent variable
The adjusted multiple coefficient of determination is adjusted for the
number of independent variables.
In an analysis of variance, one estimate of σ2 is based upon the differences between the treatment means and the
overall sample mean
The process of allocating the total sum of squares and degrees of freedom to the various components is called
partitioning.
SST = 1434. SSR = SST - SSE = 1434 - 505.98 = 928.02
prediction interval estimate
The required condition for using an ANOVA procedure on data from several populations is that the
sampled populations have equal variances.
When interpreting a correlation coefficient of .93, you would say that there is a _____ linear relationship between x and y.
strong positive
If we are testing for the equality of three population means, we should use the
test statistic F.
In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then
the estimated regression line intercepts the positive y-axis.
In the analysis of variance procedure (ANOVA), "factor" refers to
the independent variable.
The ANOVA procedure is a statistical approach for determining whether or not the means of _____ are equal.
three or more populations
To calculate the residual, you would take
yi-y^ Residual = Observed - Predicted
In a multiple regression model, the error term ε is assumed to be a random variable with a mean of
zero
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. Treatment Observations A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 The null hypothesis for this ANOVA problem is
μ1 = μ2 = μ3.
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.