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

Question

dozen eggs
1.01
.94
.89
1.03
.88
.92
.86
.93
.92
.92
milk
2.85
2.85
2.76
2.85
2.89
2.91
2.93
2.89
2.94
2.95

the regression line equation is -3.1163-0.2519x

If the price of eggs differs by .20 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.

Answer 1

The regression line equation provided is:

\[ \text{Milk Price} = -3.1163 - 0.2519 \times (\text{Egg Price}) \]

In this context, the coefficient of -0.2519 indicates the expected change in the price of milk for a unit change in the price of eggs.

If the price of eggs changes by $0.20, we can find the expected change in the price of milk by multiplying the change in eggs by the coefficient:

\[ \text{Change in Milk Price} = -0.2519 \times (\text{Change in Egg Price}) \]

Substituting in the change in egg price, we get:

\[ \text{Change in Milk Price} = -0.2519 \times 0.20 \]

Calculating this value:

\[ \text{Change in Milk Price} = -0.05038 \]

Rounding to two decimal places, the expected change in the price of milk is:

\[ \text{Change in Milk Price} \approx -0.05 \]

Thus, if the price of eggs differs by $0.20 from one month to the next, you would expect the price of milk to differ by approximately $0.05.

Answer 2

Predict the price of milk in a month when the price of eggs is 1.80. Round the answer to two decimal places.

Answer 3

To predict the price of milk when the price of eggs is $1.80 using the regression equation:

\[ \text{Milk Price} = -3.1163 - 0.2519 \times (\text{Egg Price}) \]

we substitute \( \text{Egg Price} = 1.80 \):

\[ \text{Milk Price} = -3.1163 - 0.2519 \times 1.80 \]

First, calculate \( 0.2519 \times 1.80 \):

\[ 0.2519 \times 1.80 = 0.45342 \]

Now substitute this value back into the equation:

\[ \text{Milk Price} = -3.1163 - 0.45342 \]

Now compute:

\[ \text{Milk Price} = -3.1163 - 0.45342 = -3.56972 \]

Since we are estimating the price, we need to round to two decimal places:

\[ \text{Milk Price} \approx -3.57 \]

However, a negative price doesn't make sense in the context of actual prices. This indicates that a price of $1.80 for eggs may be outside the reasonable range of the data used to create this regression model. Regression models often work best within the range of the data they were based on.

If you want an approximate value despite this, the calculation gives approximately $-3.57, which suggests that the model may not predict accurately at this price point.