Question

Which of the following correlation values represents the strongest linear relationship between two quantitative variables?

A)-1.0

B) 0

C) .90

D) -.68 A set of test scores are normally distributed. Their mean is 100 and the standard deviation is 120. These scores are converted to standard normal z-scores. What would be the mean and median of this standardized normal distribution? A) 1 B) 0 C) 100 D) 50 Suppose the correlation between two variables, math attitude (x) and math achievement (y) was found to be .78. Based on this statistic, we know that the proportion of the variability seen in math achievement that can be predicted by math attitude is: a .22 b 1.56 c .78 d .61 Which of the following numbers will be higher, the correlation between X & Y (assuming that the correlation between X & Y is a positive value) or the proportion of the variability in Y that is explained by X? a There is no way to tell; these two items are not related. b The correlation will be higher. c They will be the same. d The proportion of the variance explained will be higher.

Answer 1

Q.1) strongest linear relationship between two quantitative variables is -1

Answer: A) -1.0

Q.2) In normal distribution, mean = median = mode

If we convert the normal distributed scores into standard normal z-score then it follows, normal with mean = 1 and standard deviation = 1

That is, Z ~ N(0, 1)

Therefore,  the mean and median of this standardized normal distribution is 0

Answer: B) 0

Q.3) Given that, correlation ( r ) between X and Y is 0.78

Therefore, proportion of variablity is

r * r = r² = (0.78)² = 0.6084 = 0.61

Answer: d) 0.61

Q.4) since, correlation is lies between -1 to 1 that is,

-1 <= r <= 1

In this case we assume thatvthe correlation between C and Y is a positive value that is r > 0 )

and proportion of variability lies between 0 to 1

That is 0 <= r² <= 1

Therefore, if we square the correlation term then it will be less. Suppose r = 0.6 then r² = (0.6)² = 0.36

Hence, the value of correlation is higher.

Answer: b) The correlation is higher.