Sample Final Exam - Sample Final Exam 1 What is the ANOVA...

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Sample Final Exam 1. What is the ANOVA test? What is its relation to the T-test? (5%) In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes t-test to more than two groups. ANOVAs are helpful because they possess an advantage over a two- sample t-test. Doing multiple two-sample t-tests would result in an increased chance of committing a type I error. For this reason, ANOVAs are useful in comparing three or more means. A t-test is any statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is supported. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. When the scaling term is unknown and is replaced by an estimate based on the data, the test statistic (under certain conditions) follows a Student's t distribution. 2. What is correlation coefficient between two sets of numbers? What can you say when the correlation coefficient is zero? (Why)? (10%) All correlation coefficients range from -1.00 to +1.00. A correlation coefficient of -1.00 tells you that there is a perfect negative relationship between the two variables. This means that as values on one variable increase there is a perfectly predictable decrease in values on the other variable. In other words, as one variable goes up, the other goes in the opposite direction (it goes down). A correlation coefficient of +1.00 tells you that there is a perfect positive relationship between the two variables. This means that as values on one variable increase there is a perfectly predictable increase in values on the other variable. In other words, as one variable goes up so does the other. A correlation coefficient of 0.00 tells you that there is a zero correlation, or no relationship, between the two variables. In other words, as one variable changes (goes up or down) you can’t really say anything about what happens to the other variable.
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3. State the conditions i.e., assumptions of simple-linear regression and explain how do you check against these assumptions. (15%) There are four principal assumptions which justify the use of linear regression models for purposes of prediction: (i) Linearity of the relationship between dependent and independent variables (ii) Independence of the errors (no serial correlation) (iii) Homoscedasticity (constant variance) of the errors (a) Versus time (b) Versus the predictions (or versus any independent variable) (iv) Normality of the error distribution.
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