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​.