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Aneli [31]
3 years ago
13

When utilizing ANOVA, what does the between group sum of squares measure?

Mathematics
1 answer:
zhenek [66]3 years ago
5 0

Answer:

b. The sum of the squared deviations between each group mean and the mean across all groups

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Solution to the problem

If we assume that we have p groups and on each group from j=1,\dots,p we have n_j individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2

And we have this property

SST=SS_{between}+SS_{within}

As we can see the sum of squares between represent the sum of squared deviations between each group mean and the mean across all groups.

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

So then the best option is:

b. The sum of the squared deviations between each group mean and the mean across all groups

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A number is divided by 3. Then 14 is added to the quotient. The result is 33. What is the orginal number?
seropon [69]

let "a number" = x

a number is divided by 3 => x/3

14 is added to the quotient => (x/3) + 14

The result is 33 => " = 33"

Solve for x

(x/3) + 14 = 33

Isolate the x. Note the equal sign. What you do to one side you do the other.

Subtract 14 from both sides

(x/3) + 14 (-14) = 33 (-14)

x/3 = 19

Isolate the x. Multiply 3 to both sides

x/3(3) = 19(3)

x = 19(3)

x = 57

57 is your original number

hope this helps

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2 years ago
a culture started with 6,000 bateria after 6 hours,it grew to 7,200 .predict how many bacteria will be present after 17 hours ro
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Answer:

10058

Step-by-step explanation:

The equation is of the form

y = ab^x

Where a is the initial value, y is the final  amount and x is the time

y = 6000 b^x

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Divide each side by 6000

7200/6000 =  b^6

1.2 = b^6

Take the 6th root on each side

1.2 ^ 1/6 = b^6 ^ 1/6

1.030853321 = b

y = 6000 (1.030853321) ^ x

Let x = 17

y = 6000 (1.030853321) ^ 17

y=10057.68696

Rounding to the nearest whole number

y = 10058

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Hey there!

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