A set of n = 25 pairs of scores ( X and Y values) in a research study has a Pearson correlation of r = 0.80. What percentage of the variance for the Y scores is predicted by its relationship with X?   a. 80%   b. 20%   c. 36%   d. 64%

14.36 Ecological correlation. Many studies reveal a positive correlation between income and number of years of education. To investigate this, a researcher makes two plots. Plot 1: Plot the number of years of education (the explanatory variable) versus the average annual income of all adults having that many years of education (the response variable). Plot 2: Plot the number of years of education (the explanatory variable) versus the individual annual incomes of all adults (the response variable).

A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced Sprout Percent 45.5 65 53 62 48 44 65.5 51 58 66 42 64 62 56 Round to 2 decimal places. Find the correlation coefficient: r = The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ? 0 The p-value is: (Round to four decimal places) Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds. O There is statistically insignificant…

A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below.   Seeds Produced 65 51 59 66 42 62 61 69 65 Sprout Percent 64.5 65.5 64.5 49 72 61 50.5 54.5 50.5   Find the correlation coefficient:  r=r=    Round to 3 decimal places. The null and alternative hypotheses for correlation are:H0:H0:      == 0H1:H1:       ≠≠ 0    The p-value is:  ?  (Round to 5 decimal places) r2 = ? (Round to 3 decimal places)