For a multiple linear regression to have a multiple correlation coefficient of 1, which of these conditions is mathematically necessary? I. Every predictor has a high marginal correlation with the dependent variable. II. The predictors have low correlations with one another.
Neither condition Inor II is necessary
Neither condition is necessary. For example, let X1 = Z + U and X2 = Z − U, with independent Z and U and variance of Z much larger than variance of U. Then X1 and X2 are highly correlated and each correlates weakly with Y = U, yet Y = (X1 − X2)/2 is predicted exactly. Multiple correlation depends on their combined linear prediction.
Important Questions from Measurement and Analysis of Data - Teaching
Type II error in hypothesis testing is:
Which level of measurement is least used in educational psychology?
In List I types of variables are given and in List II correlation coefficients related to them are given. Match List I and List II and choose the correct answer from the code given below.
List I
(Types of variable)
List II
(Correlation coefficient)
a) Both variables continuous i) Biserial b) Both with ordinal measure ii) Pearson's 'r' c) Both with artificial dichotomy iii) Contingency coefficient d) One continuous and other with artificial dichotomy iv) Spearman's rho e) Two or more categories v) Tetrachoric 'r' vi) Point-Biserial Match the measurement scales in Set I with the examples in Set II.
Set I
(a) Nominal scale
(b) Ordinal scale
(c) Interval scale
(d) Ratio scaleSet II
(i) Ranking students’ performances in musical events
(ii) Spelling-test scaled scores defined with equal units and an arbitrary zero
(iii) Classifying students by the type of co-curricular activity they participate in
(iv) Students’ writing speed in words per minuteFor scores drawn from a continuous reference distribution, what is the shape of the distribution of their percentile ranks?
