1. Based on the data shown below, calculate the correlation coefficient (to three decimal places) 2. y = x + 3. A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: Use this to predict the number of situps a person who watches 1.5 hours of TV can do (to one decimal place) 4. What is the correlation coefficient for this data set? 5. Find the correlation coefficient and report it accurate to three decimal places. What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a percentage accurate to one decimal place. 6. The following bivariate data set contains an outlier. What is the correlation coefficient with the outlier? What is the
correlation coefficient without the outlier? Would inclusion of the outlier change the evidence for or against a significant linear correlation? Question for thought: Would you always draw the same conclusion with the addition of an outlier? 7. Run a regression analysis on the following
bivariate set of data with y as the response variable. What is the predicted explanatory value? 8. Rivers in North Carolina contain small concentrations of mercury that can accumulate in fish over their lifetimes. The concentration of mercury in fish tissue can be obtained by catching fish and sending samples to a lab for analysis. A study was conducted on fish from the Waccamaw and Lumber Rivers to investigate mercury levels in tissues of largemouth bass. At
several stations along each river a group of fish were caught, weighed and measured; in addition a filet from each fish was sent to a lab so that the tissue concentration of mercury could be determined. In all, 171 fish were caught at 15 different research stations along the Waccamaw and Lumber Rivers. Data from fish caught at one of these stations is shown in the following table: Compute the correlation between length and weight for these fish. (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.) 9. The line of best fit through a set of data is According to this equation, what is the predicted value of the dependent variable when the independent variable has value 150? y = Round to 1 decimal place. 10. Using your favorite
statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden. 1. The correlation coefficient is 0.992. This is only a preview of the solution. Please use the purchase button to see the entire solution By purchasing this solution you'll be able to
access the following files: How to calculate regression line?The formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.
How to calculate regression coefficient?How to Find Regression Coefficients?. To find the coefficient of X use the formula a = n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2 n ( ∑ x y ) − ( ∑ x ) ( ∑ y ) n ( ∑ x 2 ) − ( ∑ x ) 2 .. To find the constant term the formula is b = (∑y)(∑x2)−(∑x)(∑xy)n(∑x2)−(∑x)2 ( ∑ y ) ( ∑ x 2 ) − ( ∑ x ) ( ∑ x y ) n ( ∑ x 2 ) − ( ∑ x ) 2 .. |