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1.The data set shows the October 1 noon temperatures in degrees Fahrenheit for a particular city in each of the past 6 years.

76, 71, 78, 61, 85, 73

a. What is the five-number summary of the data set?

b. What is the mean, x , of the data set?

c. What is the sum of the squares of the differences between each data value and the mean? Use the table to organize your work.

What is the standard deviation of the data set? Use the sum from Part (c) and show your work

A linear model for the data in the table is shown in the scatter plot.

a   Which two points should you use to find the equation of the model? Circle the points on the graph.

b   What is the slope of the linear model?

c   What is the equation of the linear model in point-slope form?

d   What is the slope-intercept form of the equation you wrote in Part (c)?

e   What is the equation for the least squares regression line? Round the values for a and b to three decimal places.

Guest Dec 19, 2017
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#1
+80910
+1

First one

a.

Order the data from low to high

61, 71, 73, 76, 78, 85

Minimum  =  61

Median  = Q2 =  [73 + 76 ] / 2  =  149/2  =  74.5

Q1   = [61 + 71 ] / 2  =  132/2  =  66

Q3 = [ 78 + 85 ] / 2  =  76.5

Max  =  85

b.   Mean   =  [ 61+ 71+ 73+ 76 + 78+ 85] / 6   =  444/6  =  74

c.      61  -  74          - 13                169

71 -  74           - 3                      9

73 -  74           - 1                      1

76 -  74             2                       4

78  - 74             4                     16

85  - 74            11                   121

Sum      320

d. Standard  deviation  =   √ [320 / 5 ]  =  √64   =  8

CPhill  Dec 19, 2017
#2
+80910
+1

Second one

a. (7,6)  and (1,12)  best model the data

b.   Slope  =  [ 12 - 6 ]  / [ 1 - 7 ]  =  6 / -6  =  -1

c.  Point-slope form     y - 6  =  -1  (x - 7 )

d. Slope-intercept form      y  =  -1x  +  13

e.  Least squares  equation  :

y = -1.0357142857143x + 13.142857142857

Notice that this is very close to the slope-intercept form !!!!

CPhill  Dec 19, 2017

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