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Paul [167]
3 years ago
10

You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You al

so know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?
Mathematics
1 answer:
Naddika [18.5K]3 years ago
5 0

Answer:

y = 7.8x + 26

Step-by-step explanation:

Given the following :

Pearson's r = 0.78

Average consumption of ice cream = 5 grams per week (m) with Standard deviation (sd) = 1.5 grams

Average weight = 65 kg with standard deviation of 15kg

Formular for the regression line :

General regression formula :

y = mx + c

y = predicted variable ; m = slope or gradient ; x = predictor variable ; c = intercept

Gradient (m) = change in y / change in x

m = (sd y / sd x) * r

m = (sd weight / sd ice cream) × r

m = (15 / 1.5) × r

m = 10 × 0.78 = 7.8

Intercept:

mean of weight(y) - [Slope×mean of icecream(x)]

65 - [7.8 × 5]

65 - 39 = 26

Hence,

y = 7.8x + 26

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Neporo4naja [7]
Let us assume the first even number = n
The second consecutive even number = n + 2
The third consecutive even number = n + 4
The addition of the three consecutive even numbers is 42 and it is already given in the question. Based on the information's given in the question, the answer can be easily deduced.
Then, the equation can be written as
n + (n + 2) + (n + 4) = 42
3n + 6 = 42
3n = 42 - 6
3n = 36
n = 36/3
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So
The first even number = 12
The second consecutive even number = n + 2
                                                               = 12 + 2
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The third consecutive even number = n + 4
                                                           = 12 + 4
                                                           = 16
So the three consecutive even numbers are 12, 14, 16.
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