Question

True or false:

1. The correlation coefficient and the covariance of two variables can have different signs. (True or False)

2. Graphical analysis is a useful tool that allows the researcher to have an idea of the distribution of a data series. (True or False)

3. A large data samples are usually normally distributed. (True or False)

4. The standard deviation is always smaller than the variance. (True or False)

Answer 1

1) False .

Yes, the covariance and correlation coefficient between two variables will always have the same sign. Both correlation and covariance indicates if 2 variables are inversely or directly related .Example if consumer income increase,s then sale of product x also increases which indicates 2 variables are positively related and move in same direction . However , if 2 variables are negatively related then they will move in opposite direction . Example if Price increases then sale of product Y drops .

COV(x, y) =L1 n-1

x = the independent variable
y = the dependent variable
n = number of data points in the sample
= the mean of the independent variable x
= the mean of the dependent variable y

While covariance mentions how 2 variables are related positively or negatively while correlation defines the degree to which they are related and move together which is not possible to measure in covariance. Correlation coefficient is measured between value of -1 to 1 .

If coefficient is -1 then it means that 2 variables are inversely related . More it moves towards -1 more strongly it is inversely related and vice versa .

If it is 0 it means they are not related .

if it is 1 then it means both are positively related .

Formula is r_(x,y) = Cov(x,y)/sx*sy

r_(x,y) = correlation of the variables x and y
COV(x, y) = covariance of the variables x and y
s_x = sample standard deviation of the random variable x
s_y = sample standard deviation of the random variable y

2, True : It is a set of vertices and edges which represents data which correlates different data sets and provide meaningful insights about 2 or more variables ,

3. True Normal distribution means that data near mean are more frequent in occurance and as sample size increases, the standard deviation of the means decreases and vice versa .

4.True as SD is square root of variance and it means how disperse the data set is from mean . While both means that how far your data set is dispersed from mean while variance is measured in sq units but standard deviation is sq root of the variration .

Answer 2

ANSWERS :

1.  False.

( r = cov. (x y) / (s (x) * s(y)) .

s(x) and s(y) being positive always, r and cov.(x y)  will have same sign)

2. True.

(Graphical picture of data gives an idea to type of distribution which is helpful in further analysis.)

3. True .

( Large data approaches normal distribution and error factor gets reduced).

4. True.

(SD is square root of variance and hence always smaller than the variance)