Find the line that best fits the given points. and compute the correlation coefficient r. (Round all numerical values to three decimal places.) (-2, -1), (1, 1), (0, 1), (1, 2), (2, 4), (3, 3) y(x) = Compute the correlation coefficient r. (Round your answer to three decimal places.) r=

Help!!   Step 5: Calculate the correlation coefficient  ?=∑(zxi⋅zyi)n−1

Use the data in the table, which shows the average annual salaries (both Apply what you have learned in the previous 2 tab to complete this graded lab questions. in thousands of dollars) for public school principals and teachers in the U.S. for 11 years. 3 4 R Principals x Teachers y 0.9975 1. Repeat the steps from tab #1 using this data to construct a scatter plot graph and calculate the correlation coefficient R. (Recall the correlation coefficient is R and not R2) 5 77.8 43.7 6 78.4 43.8 Teachers y R= 7 80.8 80.5 81.5 45.0 45.6 8 2. Does the R value represent a positive, negative or no correlation between the 45.9 9 60.0 84.8 87.7 salaries of the teachers and principals? As teacher salaries increase, what happens to prinicipal salaries? 48.2 y-0.5873x - 2.0507 R=0.995 10 49.3 11 91.6 51.3 50.0 93.6 52.9 54.4 3. Write the equation of the regression line for the data below. The equation is y= 12 95.7 95.7 13 54.2 40.0 14 4. Use the regression equation that you found in exercise #3 to…

If variable X remains constant as variable Y decreases, the correlation is said to be: zero negative positive strong

Number 2. Provide a detailed solution.

Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. Then calculate it again, letting Row 2 represent the x-values and Row 1 the y-values. What effect does switching the variables have on r? Row 1 19 23 31 49 51 70 79 Row 2 156 155 190 141 202 191 181 Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. r= 0.430 (Round to three decimal places as needed.) Calculate the correlation coefficient r, letting Row 2 represent the x-values and Row 1 the y-values. (Round to three decimal places as needed.)

Step 5. Calculate the correlation coefficient.

Y 2. Describe the direction and strength of the correlations from the following scatterplots. (Are they weak, moderate, strong, or no correlation? Positive, negative, or no correlation?) X X X Y

Which of the following sets of data represent valid functions? R={(−5,−4),(3,2),(5,4),(7,9),(13,10)}R={(-5,-4),(3,2),(5,4),(7,9),(13,10)} F={(−4,0),(2,3),(5,6),(8,9),(16,10)}F={(-4,0),(2,3),(5,6),(8,9),(16,10)} S={(−5,−1),(2,1),(4,5),(−5,−1),(11,13)}S={(-5,-1),(2,1),(4,5),(-5,-1),(11,13)} G={(−5,0),(3,1),(3,4),(8,9),(10,12)} Which of the following sets of data represent valid functions? S={(−1,−2),(3,2),(6,4),(−1,−2),(16,13)}S={(-1,-2),(3,2),(6,4),(-1,-2),(16,13)} F={(−1,−5),(2,1),(4,6),(8,9),(12,16)}F={(-1,-5),(2,1),(4,6),(8,9),(12,16)} R={(−5,−4),(1,2),(4,5),(8,7),(12,10)}R={(-5,-4),(1,2),(4,5),(8,7),(12,10)} G={(−1,−2),(3,1),(3,5),(8,7),(14,16)}G={(-1,-2),(3,1),(3,5),(8,7),(14,16)}

Calculate the correlation coefficient​ r, letting Row 1 represent the​ x-values and Row 2 the​ y-values. Then calculate it​ again, letting Row 2 represent the​ x-values and Row 1 the​ y-values. What effect does switching the variables have on​ r?   Row 1,x Row 2,y 13 115 24 120 30 180 48 116 56 173 61 160 79 146