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21. Price of eggs and milk: The following table presents the average price in dollars for dozeneggs and a gallon of milk for each month from January through December 20 Dozen Eggs Gallon of Milk 1.94 3.58 1.80 3.52 1.77 3.50 1.83 3.47 1.69 3.43 1.67 3.40 1.65 3.43 1.88 3.47 1.89 3.47 1.96 3.52 1.96 3.54 2.01 3.58 Source: Bureau of Labor Statistics a. Compute the least-squares regression line for predicting the price of milk from the price of eggs. b. If the price of eggs differs by $0.25 from one month to the next, by how much would you expect the price of milk to differ? c. Predict the price of milk in a month when the price of eggs is $1.95.

          
            21. Price of eggs and milk: The following table presents the average price in dollars for
dozeneggs and a gallon of milk for each month from January through December 20
Dozen Eggs Gallon of Milk
1.94
3.58
1.80
3.52
1.77
3.50
1.83
3.47
1.69
3.43
1.67
3.40
1.65
3.43
1.88
3.47
1.89
3.47
1.96
3.52
1.96
3.54
2.01
3.58
Source: Bureau of Labor Statistics
a. Compute the least-squares regression line for predicting the price of milk from the
price of eggs.
b. If the price of eggs differs by $0.25 from one month to the next, by how much would
you expect the price of milk to differ?
c. Predict the price of milk in a month when the price of eggs is $1.95.

21. Price of eggs and milk: The following table presents the average price in dollars for
dozeneggs and a gallon of milk for each month from January through December 20
Dozen Eggs Gallon of Milk
1.94
3.58
1.80
3.52
1.77
3.50
1.83
3.47
1.69
3.43
1.67
3.40
1.65
3.43
1.88
3.47
1.89
3.47
1.96
3.52
1.96
3.54
2.01
3.58
Source: Bureau of Labor Statistics
a. Compute the least-squares regression line for predicting the price of milk from the
price of eggs.
b. If the price of eggs differs by 0.25 from one month to the next, by how much would
you expect the price of milk to differ?
c. Predict the price of milk in a month when the price of eggs is1.95.

Added by Elizabeth G.

Instant Answer

Step 1

This line is represented by the equation y = mx + b, where y is the dependent variable (price of milk), x is the independent variable (price of eggs), m is the slope of the line, and b is the y-intercept. To calculate m (slope), we use the formula: m = (NΣxy - Show more…

Show all steps

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Transcript

00:01 Hey there, welcome to numerate.

00:03 So for this problem here, we are looking at the average price of dozen eggs and a gallon of milk here.

00:10 And for part a, we're asked to find the least squares regression equation.

00:16 So therefore, our format for this regression equation equals y predictor equals b, x, where b is the slope, plus a where a's the y intercept.

00:31 So let's find the sum of squares first.

00:33 The sum of squares of x is equivalent to the sum of x minus this mean.

00:42 So i went on ahead and calculated a mean, which is around 1 .84 and squared.

00:52 Given us a sum of squares of x that equals around 0 .166.

01:02 All right.

01:03 So with this, we can also find a sum of products.

01:06 Sum of products is equivalent to the sum of x minus is mean times y minus is mean 3 .49.

01:21 All right.

01:35 So we calculate this and see what we get.

01:41 We get a sum of products that equals around 0 .066.

01:49 Therefore, we're going to find our slope first, the b coefficient, which is equivalent to, the sum of products divided by the sum of squares of x.

02:04 We plug in our values here and we get a slope of around 0 .399 .9.

02:23 All right.

02:24 So 0 .399.

02:27 And for our y intercept, which is the a coefficient, is equivalent to the y mean minus the slope times x mean, which gives us a value of around 2 .759.

02:44 Therefore, our overall regression equation here is y predictor equals 0 .399 x plus 2 .759.

03:05 Okay...