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Question 1

The strength (degree) of the correlation between a set of independent variables X and a dependent variable Y is measured by

A

Coefficient of Correlation

B

Coefficient of Determination

C

Standard error of estimate

D

All of the above

Question 2

The percent of total variation of the dependent variable Y explained by the set of independent variables X is measured by

A

Coefficient of Correlation

B

Coefficient of Skewness

C

Coefficient of Determination

D

Standard Error or Estimate

E

Multicollinearity

Question 3

A coefficient of correlation is computed to be -0.95 means that

A

The relationship between two variables is weak.

B

The relationship between two variables is strong and positive

C

The relationship between two variables is strong and but negative

D

Correlation coefficient cannot have this value

Question 4

Let the coefficient of determination computed to be 0.39 in a problem involving one independent variable and one dependent variable. This result means that

A

The relationship between two variables is negative

B

The correlation coefficient is 0.39 also

C

39% of the total variation is explained by the independent variable

D

39% of the total variation is explained by the dependent variable

Question 5

Relationship between correlation coefficient and coefficient of determination is that

A

both are unrelated

B

The coefficient of determination is the coefficient of correlation squared

C

The coefficient of determination is the square root of the coefficient of correlation

D

both are equal

Question 6

Multicollinearity exists when

A

independent varialbes are correlated less than -0.70 or more than 0.70

B

An independent variables is strongly correlated with a dependent variable.

C

There is only one independent variable

D

The relationship between dependent and independent variable is non-linear

Question 7

If "time" is used as the independent variable in a simple linear regression analysis, then which of the following assumption could be violated

A

There is a linear relationship between the independent and dependent variables

B

The residual variation is the same for all fitted values of Y

C

The residuals are normally distributed

D

Successive observations of the dependent variable are uncorrelated

Question 8

In multiple regression, when the global test of significance is rejected, we can conclude that

A

All of the net sample regression coefficients are equal to zero

B

All of the sample regression coefficients are not equal to zero

C

At least one sample regression coefficient is not equal to zero

D

The regression equation intersects the Y-axis at zero.

Question 9

A residual is defined as

A

$Y-\hat{Y}$

B

Error sum of square

C

Regression sum of squares

D

Type I Error

Question 10

What test statistic is used for a global test of significance?
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A

Z test

B

t test

C

Chi-square test

D

F test

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Question 1

Correlation Coefficient values lies between

A

-1 and +1

B

0 and 1

C

-1 and 0

D

None of these

Question 2

If r_{xy} = -0.84 then r_{yx}=?

A

-0.84

B

0.84

C

0.42

D

None of these

Question 3

In correlation both variables are always

A

Random

B

Non Random

C

Same

D

None

Question 4

If two variables oppose each other then the correlation will be

A

Positive Correlation

B

Zero Correlation

C

Perfect Correlation

D

Negative Correlation

Question 5

A perfect negative correlation is signified by

A

0

B

1

C

0.5

D

-1

Question 6

The correlation coefficient between U=X and V=-X is

A

+1

B

-1

C

0

D

0.5

Question 7

The correlation coefficient between X and X is

A

-1 to +1

B

0

C

-1

D

1

Question 8

The correlation coefficient r is independent of

A

Origin only

B

Scale of Measurement only

C

Both change of origin and scale of measurement

D

None of these

Question 9

If X and Y are independent to each other, the coefficient of correlation is

A

-1

B

0

C

+1

D

None

Question 10

If b_{yx }<0 and b_{xy} =<0, then r is

A

=0

B

<0

C

>0

D

≠ 0

Question 11

If r=0.6, b_{yx}=1.2 then b_{xy}=?

A

0.3

B

0.2

C

0.72

D

0.40

Question 12

When regression line passes through the origin then

A

Regression coefficient is zero

B

Correlation is zero

C

Intercept is zero

D

Association is zero

Question 13

Two regression lines are parallel to each other if their slope is

A

Different

B

Same

C

Negative

D

None of these

Question 14

When b_{xy} is positive, then b_{yx} will be

A

Positive

B

Negative

C

Zero

D

One

Question 15

If $\hat{Y}=a\,$ then r_{xy}

A

$b_{xy}=1$

B

$b_{yx}=-1$

C

$b_{yx}=0$

D

None of these

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Question 1

If all the values fall on the same straight line and the line has a positive slope then what will be the value of the correlation coefficient ‘r’:

A

0 ≤ r ≤ 1

B

r ≥ 0

C

r = +1

D

r = -1

E

0

Question 2

For a Least Square trend $\hat{Y}=\alpha +\beta X$

A

$\sum Y =\sum \hat{Y}$

B

$\sum \hat{Y}=0$

C

$\sum Y< \sum \hat{Y}$

D

$\sum Y > \sum \hat{Y}$

E

None

Question 3

In Regression Analysis $\sum \hat{Y}$ is equal to

A

0

B

ΣY

C

a

D

bX

E

None

Question 4

Which one is equal to explained variation divided by total variation?

A

Sum of squares due to regression

B

Coefficient of Determination

C

Standard Error of Estimate

D

Coefficient of Correlation

Question 5

In Regression Analysis two regression lines intersect at the point

A

(0, 0)

B

(α, α)

C

(X, Y)

D

$(\bar{X},\bar{Y})$

E

None

Question 6

If a straight line is fitted to data, then

A

$\sum Y = \sum \hat{Y}$

B

$\sum Y > \sum \hat{Y}$

C

$\sum Y < \sum \hat{Y}$

D

$\sum(Y-\hat{Y})^2=0$

Question 7

Regression Line always passes through

A

(X, Y)

B

$(\alpha, \beta)$

C

$(\bar{X},\bar{Y})$

D

$(\bar{X},Y)$

E

None

Question 8

The best fitting trend is one for which the sum of squares of error is

A

Zero

B

Minimum (Least)

C

Maximum

D

None

Question 9

In a Least Square Regression line the quantity $\sum(Y-\hat{Y})\,$ is always

A

Negative

B

Zero

C

Positive

D

Fractional

E

None

Question 10

In Least Square Regression Line $\sum(Y-\hat{Y})^2\,$ is always

A

Negative

B

Zero

C

Non-Negative

D

Fractional

E

None

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Question 1

The method of least squares finds the best fit line that _____ the error between observed and estimated points on the line

Student and Instructor of Statistics and business mathematics.
Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan.

Like Applied Statistics and Mathematics and Statistical Computing.
Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel.

Like to use type-setting LaTeX for composing Articles, thesis etc.

In early civilizations, the number of animals (sheep, goat, and camel etc.) or children people have were tracked by using different methods such as people match the number of animals with the number of stones. Similarly, they count the number of children with the number of notches tied on a string or marks on a […]

The Z-Score The Z-score also referred to as standardized raw scores is a useful statistic because not only permits to compute the probability (chances or likelihood) of raw score (occurring within normal distribution) but also it helps to compare two raw scores from different normal distributions. The Z-score is a dimensionless measure since it is […]

Multicollinearity in Linear Regression Models The objective of multiple regression analysis is to approximate the relationship of individual parameters of a dependency, but not of interdependency. It is assumed that the dependent variable and regressors ‘s are linearly related to each other (Graybill, 1980; Johnston, 1963 and Malinvaud, 1968). Therefore, inferences depicted from any regression […]

Levels of Measurement (Scale of Measure) Level of measurement (scale of measure) have been classified into four categories. It is important to understand these level of measurement, since these level of measurement play important part in determining the arithmetic and different possible statistical tests that are carried on the data. The scale of measure is […]

Variance is a measure of dispersion of a distribution of a random variable. The term variance was introduced by R. A. Fisher in 1918. The variance of a set of observations (data set) is defined as the mean of the squares of deviations of all the observations from their mean. When it is computed for […]

Reading and Writing Data in R Reading Data in R For reading (importing) data into R following are some functions. read.table(), and read.csv(), for reading tabular data readLines() for reading lines of a text file source() for reading in R code files (inverse of dump) dget() for reading in R code files (inverse of dput) […]

In R language, list is an object that consists of an ordered collection of objects known as its components. A list in R Language is a structured data that can have any number of any modes (types) of other structured data. That is, one can put any kind of object (like vector, data frame, character […]

The R program’s structure is similar to the programs written in other computer languages such as C or its successors C++ and Java. However, important differences between these languages and R are (i) R has no header files, (ii) most of the declarations are implicit, (iii) there are no pointers in R, and (iv) text […]

The problem of multicollinearity plagues the numerical stability of regression estimates. It also causes some serious problem in validation and interpretation of the regression model. Consider the usual multiple linear regression model, , where is an vector of observation on dependent variable, is known design matrix of order , having full-column rank , is vector of […]

R language provides an interlocking suite of facilities that make fitting statistical models very simple. The output from statistical models in R language is minimal and one needs to ask for the details by calling extractor functions. Defining Statistical Models; Formulae in R Language The template for a statistical model is a linear regression model […]

Source Code of R Method There are different ways to view the source code of an R method or function. It will help to know how function is working. Internal Functions If you want to see the source code of internal function (functions from base packages), just type the name of the function at R prompt such […]

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TEST 4, Q.1 – I THINK THE ANSWER SHOULD BE (D)-PARALLEL TO X-AXIS

Test 4, Q.7. Thank you. Correction is made.