Below is a set of observations for two variables, x and y.   x Y 1 3 2 7 3 5 4 11 5 14 a.) Develop a scatter diagram by hand b.) Calculate the mean and standard deviation of x c.) Calculate the mean and standard deviation of y d.) Calculate the covariance e.) Calculate the correlation coefficient Please do not use excel or spss, I need to see how these are done by hand

14) For the data below, determine the value of the linear correlation coefficient r between y and x. 14 x 1.2 2.7 4.4 6.6 9.5 y 1.6 4.7 9.9 24.5 39.0 A) 0.913 B) 0.985 C) 0.990 D) 0.873

Match the following choices with the given diagrams. A. Positive linear correlation B. Negative linear correlation C. No linear correlation 10 20 y 20 y 10 10 40 2- -50 10

1. A medical student is studying heart rate. The student wants to know if there relationship between age and heart rate. She collects the following data from children selected at random. Heart rate Age (yrs) 92 89 90 84 79 102 108 12 86 14 a) Make a scatter plot of the data. b) Describe the relationship(positive, negative and none) you see between heart rate and age and determine the type of correlation (linear or non-linear) that exists. Relationship Туре» c) Draw a line of best fit. d) What do you think is the heart rate of a newborn baby? Justify your answer. e) What do you think is the heart rate of someone who is 20 years old? What type of prediction is this?

Match the correlation coefficients with their scatterplots. Select the letter of the scatterplot below which corresponds to the correlation coefficient. (Click on image for a larger view.) B v 1. r = -0.74 с A ✓ 2. r = -0.49 3. r = -0.97 4. r = 0.76 A B D

Suppose the correlation between variables x and y isr = – 1. Also suppose that the data contains the points (6, 14) and (2, 18). Finally, suppose that the x-values in the data set are: æ 2 3 5 6 8 Make a scatterplot of this data set. 20+ 19 18 17 16 15 14 13 12 10 8 6 6

Match the correlation coefficients with their scatterplots. Select the letter of the scatterplot below which corre- sponds to the correlation coefficient. (Click on image for a larger view.) ? 1. r= 0.76 ? 2. r=-0.74 ? 3. r= 0.22 ? 4. r= -0.97 A B C D

3. The speed (in miles per hour) of 8 vehicles and their braking distance (in feet) when stopping on a dry surface speed, x braking distance, y 20 30 40 50 50 60 65 70 55 72 75 110 138 162 193 225 type of correlation: Conclusion

Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for public school principals and teachers in the U.S. for 11 years. Apply what you have learned in the previous tab to complete this graded lab questions. 1. Repeat the steps from tab #1 using this data to construct a scatter plot graph and calculate the correlation coefficient R. (Recall the corelation coefficient is R and not R Teachers y Principalsx 77.8 43.7 78.4 43.8 80.8 45.0 R= 80.5 45.6, 2. Does the R value represent a positive, negative or no correlation between the salaries ol the teachers and principals? As teacher salaries increase, what happens to prinicipal salaries? 10 11 81.5 45.9 84.8 48.2 12 13 87.7 49,3 3. Write the equation of the regression line for the data below. The equation is y= 14 91.6 51.3 52.9 Teachers y 15 16 95.7 54.4 COD 54.2 =D0.5873x-2.0s07o R=0.995, 17 95.7 4. Use the regression equation that you found in exercise #3 to predict the average annual salary…

A local store kept track of the number of advertisements it placed in local newspapers and the number of stereo systems it sold each week. Week 1 2 3 4 5 6 7 8 Advertisements, x 7 5 4 2 8 5 5 3 Stereos Sold, y 23 15 12 8 2 7 9 6 a) Create a scatter plot for the data showing Advertisements Vs. Stereos Sold. b) Determine the value of r, the correlation coefficient for the set of data and classify the type of correlation. c) What does this correlation coefficient suggest about the effectiveness of the advertisements? Explain