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he following table presents the average price in dollars for a dozen eggs and a gallon of milk for each month from March through December.

Dozen Eggs
1.21
1.13
1.01
1.20
1.15
1.28
1.26
1.33
1.45
1.56

Gallon of Milk
2.66
2.67
2.69
2.68
2.71
2.67
2.90
2.91
2.94
2.95

The regression line equation is y= 1.9826+0.6323x

If the price of eggs differs by $0.30 from one month to the next, by how much would you expect the price of milk to differ? Round your answer to two decimal places.

3 answers

In the regression line equation \( y = 1.9826 + 0.6323x \), \( y \) represents the price of milk, and \( x \) represents the price of eggs. The coefficient of \( x \) (which is \( 0.6323 \)) tells us the expected change in the price of milk for a one-unit change in the price of eggs.

To find out how much the price of milk would differ if the price of eggs changes by $0.30, we can multiply the change in the price of eggs by the coefficient for \( x \):

\[ \text{Change in price of milk} = 0.30 \times 0.6323 \]

Calculating this:

\[ \text{Change in price of milk} = 0.30 \times 0.6323 = 0.18969 \]

Rounding this value to two decimal places, we get:

\[ \text{Change in price of milk} \approx 0.19 \]

Therefore, if the price of eggs differs by $0.30 from one month to the next, you would expect the price of milk to differ by approximately $0.19.

Predict the price of milk in a month when the price of eggs is 1.84. Round the answer to two decimal places.

To predict the price of milk when the price of eggs is $1.84, we can use the given regression line equation:

\[ y = 1.9826 + 0.6323x \]

Here, \( x \) is the price of eggs, which is $1.84. We can substitute \( x \) into the equation:

\[ y = 1.9826 + 0.6323(1.84) \]

Now, calculate \( 0.6323 \times 1.84 \):

\[ 0.6323 \times 1.84 = 1.164712 \]

Next, add this to 1.9826:

\[ y = 1.9826 + 1.164712 = 3.147312 \]

Now, rounding this to two decimal places, we get:

\[ y \approx 3.15 \]

Therefore, the predicted price of milk when the price of eggs is $1.84 is $3.15.