STATS Exam 4 Review
A Chi Square Test of Independence can be used to test hypothesis about the proportion of the population that falls into each of the possible categories.
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A Chi Square curve is symmetrical about 0.
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A Chi Square curve starts at 0 on the horizontal axis and extends indefinitely in both directions approaching, but never touching, the horizontal axis as it does so.
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A significant positive correlation between X and Y implies that changes in X cause Y to change
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For the Chi Square test of independence, the associated p-value is the area under the appropriate chi square curve to the left of the calculated x-squared
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For the two sample t-test, we can estimate the appropriate degrees of freedom by using a conservative approach and setting the degrees of freedom to be one more than the smaller of the two sample means.
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In order to decide whether the observed data is compatible with the null hypothesis, the observed cell counts are compared to the cell counts that would be expected when the alternative hypothesis is true.
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The Chi Square Statistic becomes less accurate as the cell counts get smaller.
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The expected cell count for the row x and column y entry in a two way table is equal to the product row x and column y margin totals
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The formula for the expected cell counts used in the chi square test of independence of two variables depends on sample size.
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The notation refers to the average value of the dependent variable Y.
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The population correlation coefficient r is always between 0 and 1.
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The results from ANOVA will be approximately correct if the data are highly skewed or there are extreme outliers.
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When Y=ax+b, the expected change in the value of Y for one unit change in X is a.
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When using simple linear regression analysis, if there is a strong correlation between the independent and dependent variable, than we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.
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When we test for differences between two related means, our null hypothesis is that the mean of the one with the larger sample size is greater than the mean of the one with the smaller sample size.
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for a t-distribution, the degrees of freedom are n+1
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the formula for the degrees of freedom for the chi square test of the independence of two variables depends on sample size.
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the least squares simple linear regression line minimizes the sum of the vertical deviations
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the results from ANOVA will be approximately correct as long as the ratio of the largest standard deviation to the smallest standard deviation is greater than 2.
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A Test of Least Squares (Linear) Regression has the test statistic t.
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A correlation coefficient measures the strength of the linear relationship between the dependent variable (Y) and an independent variable (X). It is a unitless measure, therefore does not have an interpretative connotation, as does the coefficient of determination
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A factor is a variable that can be used to differentiate population groups
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A good residual plot has the following characteristic that the residuals look like a bunch randomly on a graph
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A simple linear regression model is an equation that describes the straight line relationship between a dependent variable and an independent variable.
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A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and independent variable
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A t-distribution with df > 30 is very close to a standard normal distibution
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A variable that has a Chi Square distribution can take only nonnegative values.
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After plotting data points s on a scatter diagram, we have observed an inverse relationship between the independent variable (X) and the dependent variable (Y). Therefore, we can expect both the sample slope and sample correlation coefficient to be a negative value.
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An analysis of variance or ANOVA is a method of inference used to test whether or not three or more population means are equal.
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An assumption of the Least Squares (Linear) Regression model is the mean response, uy, has a straight line relationship with x: uy=a+Bx
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An assumption of the Least Squares (Linear) Regression model is the observed response for y of any value x varies according to a normal distribution.
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An assumption of the Least Squares (Linear) Regression model is the y-values are independent of each other
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For a 95% confidence interval, t* is larger
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For a Chi Square Test of Independence with the same degrees of freedom, the larger the Chi-Square statistic, the smaller the associated p-value.
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For the two sample t test, the population standard deviations are unknown, otherwise we would use the z-distribution
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If r is negative 1, than we can conclude that there is a perfect relationship between X and Y
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If the absolute value of the test statistic is greater than the critical value, then we reject the null hypothesis.
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In a Chi Square Test for Independence, the Chi-Square test statistic measures how far the observed counts in a two way table are from the expected counts.
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In a Chi Square Test of Independence, if it turns out that the observed counts are far from the expected counts, then we would have evidence against the null hypothesis
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In a Chi Square Test of Independence, the Expected Count is the theoretical value and the Observed Count is the experimental value.
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In a Chi Square Test of Independence, the expected count is calculated by column total times row total divided by the grand total.
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In a Chi Square Test of Independence, the null hypothesis is that there is no association between the two variables in a two way table.
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In a Chi Square Test of Independence, we get trustworthy results if all expected counts are greater than one and no more than 20% of the expected counts are less than five.
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In a Chi Square test of Independence, the alternative hypothesis is an association between the variables.
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In a Chi Square test of Independence, the expected count is calculated by column total times row total divided by grand total.
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In a Chi-Square Test of Independence, if the null hypothesis is true and the cell counts are reasonably large, than the chi-square test statistic has am approximate chi-square distribution.
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In a Two Way Table, the Grand Total is the total of the counts in all the cells.
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In a simple linear regression analysis the quantity that gives the amount by which Y (dependent variable) changes for a unit change X (independent variable) is called the slope of the regression line
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In a simple linear regression analysis, the correlation coefficient () and the slope (m) always have the same size
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In a simple linear regression model, the correlation coefficient not only indicates the strength of the relationship between independent and dependent variables, but also shows whether the relationship is positive or negative.
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In a simple linear regression model, the slope term is the change in the mean value y associated with a 1 unit increase in x.
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In a simple linear regression model, the y-intercept is the mean value of y when x equals 0.
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In a simple regression analysis, if the correlation coefficient is a positive value than the slope of the regression line must also be positive
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In a statistical model on which the one way ANOVA is predicated, it is assumed that in the population, there is a homogeneity of variance across treatment groups
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In the analysis of variance (ANOVA), a factor is set of related treatments, categories, or conditions.
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In the analysis of variance (ANOVA), the measure is the dependence variable in the study.
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In the one-was ANOVA, the F-statistic is used to compare the between groups and when groups variance estimates
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In the one-way ANOVA, the degrees of freedom MS between is the number of groups minus 1.
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In the simple linear regression model, a and b are fixed numbers that are usually unknown
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In the simple linear regression model, the point estimate and point prediction are equal for a particular value of X.
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In the simple linear regression model, the standard deviation of Y is equal to the same as the standard deviation of the random deviation e.`
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Linear Regression Analysis is a statistical technique in which we use observed data to relate a dependent variable to one or more predictor (independent) variables.
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The Chi Square Test of Independence becomes more accurate as cell counts get larger.
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The coefficient of determination (R2) = xx. That is xx of the variation is explained and yy of the variation is unexplained
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The dependent variable is the variable that is being describe, predicted, or controlled
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The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.
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The least squares regression line minimizes the sum of the squared deviation between actual and predicted y values.
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The levels of a factor are the possible values of settings a factor can assume
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The name of the test statistic that results from ANOVA is F-Ratios
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The point estimate a+bx* is an unbiased statistic that can be used to estimate the mean value of y when x=x*
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The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.
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The simple linear regression model assumes there is a linear relationship between the dependent variable and independent variable
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The slope of the simple linear regression equation represents the average change in value of the dependent variable per unit change in the independent variable (x).
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The total area under a Chi Square curve is equal to 1
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Things one must check before running a regression model are linearity, normailty, and independence.
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We use the t-test when we have a small sample and don't know the sigma, the population standard deviation.
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While the range of r2 is between 0 and 1, the range for r is between -1 and 1
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William S. Gosset invented t-inference procedures
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coefficient of determination (R2) = x
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compared to the standard normal distribution, a t-distribution has more are under its tails
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correlation r = sqrt. R2
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error in regression = cannot predict Y perfectly
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for the two sample t test, our data should be approximately normal or our sample size should be big
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one assumption of the Least Squares (Linear) Regression model is the standard deviation of y, o, is the same for all values of x.
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r2 tells us the proportion of variability in Y accounted for by X
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the conservative method for finding the degrees of freedom for two population samples is two subtract one from the smaller sample size.
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the conservative method for finding the degrees of freedom from two population samples is to subtract one from the smaller sample size
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the degrees of freedom are n-1
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the estimated mean value of Y is a + bx* when X has the value of x*
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the one way ANOVA tests the hypothesis that, in the population all the group means have the same value
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the variable of interest is the response variable, which may be related to one of more factors
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the y-intercept of the simple linear regression model is the value of y when the mean value of x is 0.
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