Word Problem ANSWERS: Regression #1

As a director of counseling, you are interested in how well your therapy works. In particular, you are curious whether the number of counseling sessions is a good predictor of happiness (smiles per hour). Here is the sample you collected.

  Sessions          Happiness
       12                    4
         3                    7
         9                    2
         4                   11
         7                    9
         5                    5
         6                    9
         2                    7
         2                    9

What is the SS for Counseling:   76

What is the standard deviation of Counseling: 3.08

What is the range of Happiness:   9

What is the SS for Happiness:   66

What is the SSxy:                   – 37

Since you are interested in how well one variable acts as a linear predictor of another, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

Perform the comparison you selected in the item above. Select only the appropriate one(s). What was the result of your calculations?

a = 9.92

b =  -.49

r =

t =

F =

 If a client has 10 sessions with you, what would you predict their happiness to be?  5.05

Within what boundaries is this estimate accurate?   Plus or minus 2.62.

Note: If happiness predicted sessions, than a = 9.92, b = -.52 and standard error of estimate = 2.81.

 

 

Word Problem ANSWERS: 1-Way ANOVA #9

 You work for a bottled-water company which is concerned with the quality of its flavored product. The numbers below are the number of complaints received in a 1-hour period.

               Lemon   Lime  Orange  Root Beer 
                    12        1        18         1 
                    13        4          9         2 
                    11        5        12         1 
                    14        3          7         9

Sum X         50       13          46      13        122
Sum X²     630        51       598      87       1366
N                  4          4           4        4          16
SS                 5        8.75     69       44.75   127.50

Since you are interested in which flavor did best, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is the independent variable in this design: flavor

What is the dependent variables in this design: complaints

Based on above data, complete the following summary table:

                  SS       df          ms

Between  308.25     3      102.75

Within     127.50    12      10.63

Total       435.75    15      29.05

F = 9.67

What is the critical value for F = 3.49

Is F significant? Yes

What should be done next? t-tests

 

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Word Problem ANSWERS: 1-Way ANOVA #8

Several samples of each flavor of ice tea are taken. Which flavor tastes the best (number of complaints):

                 Peach     Strawberry   Berry
                   4                3              20  
                   7                3              19 
                   6                7                8 
                   2                4              11 
                   2                1              10

 

Sum X         21           18              68               107
Sum X²     109           64          1046             1239
N                  5             5                5                 15
SS              20.8        19.20        121.20          161.20

Since you are interested in which soft drink did best/worst, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is(are) the independent variable(s) in this design: Flavor

What is the dependent variable in this design:  Complaints

Based on above data, complete the following summary table:

                             SS        df         ms

Between          314.53      2      157.27

Within             161.20    12        13.43

TOTAL           475.73    14        33.98

What is the F for this test?   11.71

What is the critical value for F?   3.88

Is the F significant?   Yes

What should be done next?   t-tests

 

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Word Problem ANSWERS: 1-Way ANOVA #7

Several samples are taken of each flavor of cough syrup. Which flavor tastes the best (number of complaints):

    Peach     Cherry  Melon Lemonade
          4           2          4          11
          3           1          8            8
          7           7          7            3
          5           6          3            9
          2           2          7          12

 

Sum X       21        18         29         43        111
Sum X²     103        94       187      419         803
N                 5          5          5          5           20
SS              14.80  29.20    18.80   49.20    112

Since you are interested in which flavor did best, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is the independent variable in this design: flavor

What is the dependent variables in this design: complaints

Based on above data, complete the following summary table:

                      SS      df    ms

Between      74.95     3   24.98

Within        112.00   16    7.00

Total          186.95   19    9.84

F = 3.57

What is the critical value for F = 3.24

Is F significant? Yes

What should be done next?  t-tests

 

 

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Word Problem ANSWERS: 1-Way ANOVA #6

Several samples of each flavor of ice cream are taken. Which flavor tastes the best (number of complaints):

                 Tea  Vegetable  Strawberry 
                   2             5           22  
                   3             5           17 
                   1             1             6 
                   1             2           15 
                   4             3           12

 

Sum                 11          16             72            99
SumX²             31          64         1178        1273
N                       5            5               5            15
SS                      6.80     12.80      141.20     160.80

Since you are interested in which soft drink did best/worst, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is(are) the independent variable in this design:  flavor

What is the dependent variable in this design: complaints

Based on above data, complete the following summary table:

                SS       df          ms

Between  458.80     2      229.40

Within     160.80    12      13.40

Total       619.60    14      44.26

F = 17.12

What is the critical value for F?   3.88

Is the F significant?  Yes

What should be done next?  t-tests

 

 

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Word Problem ANSWERS: 1-Way ANOVA #5

 

You work for a pharmaceutical company which is testing a cure for the common cold. Each group is composed of independent groups, randomly assigned to treatment by you. The four groups differ in the number of days they have taken the drug. The numbers below are the number of sniffles in a six-month period.

   0 Days       1 Day     4 Day       6 Days
                  4            16              12               6
                  2              4                4             12
                  3            11              12               9
                  4              9              11             15
                  2              3                7             14

 

Sum         15           43              46              56              169
SumX²      49         483            474            682            1683
N                5             5                5                5                20
SS               4         133.20         50.80         54.80         222.80 

 

Since you are interested in which soft drink did best/worst, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is(are) the independent variable(s) in this design: days

What is the dependent variable in this design: sniffles

Based on above data, complete the following summary table:

                SS       df          ms

Between  185.20     3      61.73

Within     222.80    16      13.93

Total       408.00    19      21.47

F = 4.43

What is the critical value for F =  3.24

Is F significant? yes

What should be done next? t-tests

 

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Word Problem ANSWERS: 1-Way ANOVA #4

 Several samples are taken of each cookie you sell at your cookie cart. Which flavor sells best (number of cookies sold in an hour):

Coffee          Lemon        Chocolate
    3                   4                 11
    6                   1                   8
  11                   7                   7
  15                   4                 13
  12                   2                 12

 

Sum           47                18                 51            116
SumX²     535                86               547          1168
N                 5                  5                  5              15
SS              93.20           21.20          26.80        141.20

Since you are interested in which cookie did best, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is the independent variable in this design: cookie

What is the dependent variables in this design: sales

Based on above data, complete the following summary table:

                         SS         df       ms

Between        129.73       2     64.87

Within            141.20     12     11.77

TOTAL         270.93     14     19.35

What is the F for this test?  5.51

What is the critical value for F? 3.88

Is the F significant? yes

What should be done next? t-tests

 

 

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Word Problem ANSWERS: 1-Way ANOVA #3

#3

You notice that the entire population of Rhode Island seems to be influenced in odd ways by what they eat. You randomly assign them to different kinds of fruit to eat and measure how many speeding tickets they get. Consider the following data:

Apple    Orange    Peach   Blueberry
   5              8             2         24
 10              2             2         21
   7              3             3         18
   2            12             4           5
   3              7             3           7

 

Sum         27            32           14           75           148
SumX²   187          270           42       1415         1914
N               5              5             5             5             20
SS          41.20       65.20       2.80       290.00      399.20

Since you are interested in which fruit drink did best, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is the independent variable in this design: fruit

What is the dependent variables in this design: tickets

Based on above data, complete the following summary table:

                     SS         df           ms

Between        419.60      3     139.87

Within           399.20     16       24.95

TOTAL        818.80     19       43.09

What is the F for this test: 5.61

What is the critical value for this test: 3.24

Is the F significant? yes

What should be done next? t-tests

 

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Word Problem ANSWERS: 1-Way ANOVA #2

As sales manager for a large corporation, you wonder if one airline is significantly faster than another. You randomly assign your sales staff to the airlines, and measure the number of hours it takes to make the trip from Long Beach to LAX. Consider the following data:

              KnoWay    Air-Ex      FlyBy   Nifty 
                   9               6            1            4 
                 11               4            2            2 
                 16               5            4            1 
                   9             14            5            1 
                 12             17            3            7

Sum X        57           46           15          15          143
Sum X²     683          582           55         71        1371
N                 5              5             5           5            20
SS             33.20    138.80        10         26         208

Since you are interested in which soft drink did best, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is the independent variable in this design: airlines
What is the dependent variables in this design: hours it takes to make the trip
Based on above data, complete the following summary table:

                     SS          df         ms
Between      278.55      3      92.85
Within         208.00     16     13.00
Total           486.55     19     25.61

What is the F for this test: 7.14
What is the critical value for this test: 3.24
Is the F significant? yes
What should be done next? t-tests

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Word Problem ANSWERS: 1-Way ANOVA #1

You work for a bottled-water company which is concerned with the quality of its flavored product. The numbers below are the number of complaints received in a 1-hour period.

Lemon        Lime         Orange        Root Beer 
   12              1               18                 1
   13              4                 9                 2
   11              5               12                 1
   14              3                 7                 9

 

Sum           50            13                46              13               121
SumX²     630            51              598              87            1366
N                 4              4                  4                4                16
SS               5            8.75              69              44.75         127.50

Since you are interested in which flavor did best, which of the following tests should you perform:

a. t-test
b. ANOVA
c. correlation
d. regression
e. multiple regression

What is the independent variable in this design:

What is the dependent variables in this design:

Based on above data, complete the following summary table:

                SS       df          ms

Between  308.25  3  102.75

Within     127.50  12  10.63

Total       435.75  15   29.05

F =  9.67

What is the critical value for F = 3.49

Is F significant? Yes

What should be done next?  t-tests

 

 

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