Expert Q&A; Done Please explain the answer step by step l-& use the data in the

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Expert Q&A; Done Please explain the answer step by step l-& use the data in the table, which shows the average tboth in thousands of dollars) for public school counselors and public For Exercises Adapted froom Educational school librarians in the United States for 12 years. Research Service 48.2 50.0 50.0 51.7 52.3 52.5 53.7 55.9 57.6 58.8 60.1 60.2 46.7 49.0 48.7 49.6 50.4 50.7 53.3 54.9 9 58.0 59.5 59.1 Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain. . Calculate the correlation coefficient r and interpret the result. 3. Test the significance of the correlation coefficient r that you found in egression line Exercise 4 to predict the Exercise 2. Use a -0.01. Find the equation of the regression line for the data. Draw the r on the scatter plot that you constructed in Exercise 1. Use the regression equation that you found in average salary of public school counselors is $59,500 5. annual salary of public school librarians when the average annual d the coefficient of determination r and interpret the result andard error of estimate s, and interpret the result. Find the st Construct a s when the average annual salary of public school counselors school librarians is $$5,250. Interpret the results % prediction interval for the average annual salary of public

Explanation / Answer

QUESTION 2.

calculation procedure for correlation

sum of (x) = x = 651

sum of (y) = y = 636.8

sum of (x^2)= x^2 = 35507.42

sum of (y^2)= y^2 = 34013.96

sum of (x*y)= x*y = 34750.66

to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)

covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1

= 34750.66 - [ 12 * (651/12) * (636.8/12) ]/12- 1

= 17.022

and now to calculate r( x,y) = 17.022/ (SQRT(1/12*34750.66-(1/12*651)^2) ) * ( SQRT(1/12*34750.66-(1/12*636.8)^2)

=17.022 / (3.986*4.292)

=0.995

value of correlation is =0.995

coeffcient of determination = r^2 = 0.99

properties of correlation

1. If r = 1 Corrlation is called Perfect Positive Corrlelation

2. If r = -1 Correlation is called Perfect Negative Correlation

3. If r = 0 Correlation is called Zero Correlation

& with above we conclude that correlation ( r ) is = 0.995> 0 ,perfect positive correlation

( X) ( Y) X^2 Y^2 X*Y 48.2 46.7 2323.24 2180.89 2250.94 50 49 2500 2401 2450 50 48.7 2500 2371.69 2435 51.7 49.6 2672.89 2460.16 2564.32 52.3 50.4 2735.29 2540.16 2635.92 52.5 50.7 2756.25 2570.49 2661.75 53.7 53.3 2883.69 2840.89 2862.21 55.9 54.9 3124.81 3014.01 3068.91 57.6 56.9 3317.76 3237.61 3277.44 58.8 58 3457.44 3364 3410.4 60.1 59.5 3612.01 3540.25 3575.95 60.2 59.1 3624.04 3492.81 3557.82

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