Correlation and Regression
D
Correlation refers to: A. The proportion of variance that two variables share. B. The casual relationship between two variables. C. A statistical method that can only be used with a correlational research design. D. The association between two variables.
True
Error is the difference in the actual value and the predicted value. True or False
True
Errors are also called residuals. True or False
B
If the correlation coefficient is -1, which answer is correct? A. The slope of the best fit line is positive B. The data fit exactly on a line with negative slope. C. The slope of the best fit line is -1. D. The data fit exactly on a line with positive slope.
D
If two variables are highly correlated, what do you know? A. that they always go together B. that high values on one variable lead to high values on the other variable C. that there are no other variables responsible for the relationship D. that changes in one variable are accompanied by predictable changes in the other
True
In a simple linear regression model, the correlation coefficient not only indicates the strength of the relationship between independent and dependent variable, but also shows whether the relationship is positive or negative. True or False
True
In any regression model, there is implicit assumption that a relationship exists between the variable. True or False
C
In simple regression analysis, if the correlation coefficient is a positive value, then: A. The standard error or estimate can either have a positive or a negative value. B. The Y intercept must also be a positive value. C. The slope of the regression line must also be positive. D. The least squares regression equation could either have a positive or a negative slope.
B
Regression analysis was applied to return rates of Sparrow Hawk colonies. Regression analysis was used to study the relationship between return rate (x: % of birds that return to the colony in a given year) and immigration rate (y: % of new adults that join the colony per year). The following regression equation was obtained) = 31.9 - 0.34x Based on the above estimated regression equation, if the return rate were to decrease by 10% the rate of immigration to the colony would________________ A. increase by 34% B. increase by 3.4% C .decrease by 0.34% D. decrease by 3.4%
One response and one or more explanatory variables are related or more explanatory variables are related
Regression modelling is a statistical framework for developing a mathematical equation that describes how: A.one explanatory and one or more response variables are related B. several explanatory and several response variables response are related C.one response and one or more explanatory variables are related D. all of these are correct
B
A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: y = 50,000 - 8X The above equation implies that an ________ A. increase of $1 in price is associated with a decrease of $8 in sales B. increase of $8 in price is associated with an increase of $8,000 in sales C .increase of $1 in price is associated with a decrease of $42,000 in sales D. increase of $1 in price is associated with a decrease of $8000 in sales
D
A regression tries to predict student GPA percentile (on a zero-100 scale) from their SAT-Math score. You are to make the relevant prediction for a student who has a SAT math score of 600 (note that SAT scores go from 200 to 800). He would be expected to be closest to the -- percentile of GPA on the basis of the regression output below: Coefficient t-stat Intercept 20 0.3 SAT-Math 0.1 5.0 R-squared: 0.36 A. 10th percentile B. 20th percentile C. 60 th percentile D. 80th percentile E. 100th percentile
D
A researcher finds a correlation of 0.40 between personal income and the number of years of college completed. Based upon this finding he can conclude that A. a person who attended four years of college will have an annual income of PHP 40,000 B. more years of education causes higher income C .personal income is a positively skewed variable D. more years of education are associated with higher income
True
A scatter diagram is a graphical depiction of the relationship between the dependent and independent variables. True or False
B
A study is done of students commuting to a large university by bicycle. The correlation between the time spent waiting at traffic lights and total cycling time was 0.50. This means: A. The average rider spent half his cycling time waiting at traffic lights. B. The more time a rider spends waiting at traffic lights, the higher is total time is likely to be. C. If the rider's time at traffic lights increases by 5 minutes, he will spend an additional 10 minutes commuting, on the average. D. If the rider's time at traffic lights increases by 10 minutes, he will spend an additional 5 minutes commuting, on the average.
True
Correlation analysis is unable to tell how much one variable will change if another variable changes a certain amount. True or False
B
On August 3rd 50 randomly selected subjects had their systolic blood pressure (SBP) recorded twice—the first time at about 9:00 a.m. and the second time at about 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect the correlation to be (a) The correlation to be near zero, as morning and afternoon readings should be independent. (b) The correlation to be high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon. (c) The correlation to be high and negative, as those with relatively high readings in the morning will tend to have relatively low readings in the afternoon. (d) The correlation to be near zero, as correlation measures the strength of the linear association. (e) The correlation to be near zero, as blood pressure readings should follow approximately a Normal distribution.
True
The coefficient of determination takes on values between -1 or +1. True or False
C
The correlation between the average midterm score of each of 10 classes of statistics and the average final exam score was found to be 0.85. A statistics instructor conclude that if a student has a B on the midterm, he has an 85 percent chance of a B on the final. The conclusion is: a. Can't tell because of the information provided in the problem. b. Incorrect, because it is an average correlation, and there is usually much more variance of averages than of individuals. c. Incorrect, because it is an ecological correlation, which means there is usually more variance of individuals than of averages. d. Correct
True
The dependent variable is called the response variable. True or False
True
The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable. True or False
A
The unemployment rate is related to inflation by the Phillips curve, which is typically a negative sloped curve looking like a hyperbola -- inflation is very high at very low rates of unemployment, and it takes very high rates of unemployment to bring inflation down to zero. We compute a correlation coefficient between unemployment rates and inflation, and find it is negative 0.5. The true relation between the two is most probably: a. Stronger than reported by the correlation coefficient, due to the non-linearity. b. Weaker than reported by the correlation coefficient, due to the great scatter or points around the line. c. Positive d. Exactly as reported by the correlation coefficient.
False
There is no relationship between variables unless the data points lie in a straight line. True or False
B
Two lists of numbers, X and Y, have a correlation of 0.3; X and Z have a correlation of - 0.7. We know that: A. the stronger correlation is the correlation of X and Y, since it is positive. B. the stronger correlation is the correlation of X and Z. C. the two correlations are equally strong, since 1.0 - 0.7 = 0.3 D. We cannot tell which is stronger without more information.
C
Which of the following indicates the strongest relationship? A. r = 0.27 B. r = 0.09 C. r = -0.60 D. r = 0.50
