The total amount of construction spending on highways and streets​ (in billions of​ dollars) is given in the accompanying table for the first six months of 2016.

**Month**

January

February

March

April

May

June

**Spending**

9292

9090

8989

8989

8484

7373

​(a) Find the​ least-squares regression line that models these​ data, with

xequals=1

corresponding to January 2016.

Part 1

​(a) The linear model for the data is

y equals left parenthesis nothing right parenthesis x plus left parenthesis nothing right parenthesisy=enter your response herex+enter your response here.

To find the least-squares regression line for the given data, we need to model it in the form:

\[
y = mx + b
\]

Where:
- \( y \) is the spending in billions of dollars,
- \( x \) represents the months (January = 1, February = 2, etc.),
- \( m \) is the slope of the line, and
- \( b \) is the y-intercept.

Let's first summarize the dataTo find the least-squares regression line for the given data, we need to model it in the form:

\[
y = mx + b
\]

Where:
- \( y \) is the spending in billions of dollars,
- \( x \) represents the months (January = 1, February = 2, etc.),
- \( m \) is the slope of the line, and
- \( b \) is the y-intercept.

Let's first summarize the 

| **Month** (x) | **Spending** (y) |
|---------------|------------------|
| 1 (January)   | 9292             |
| 2 (February)  | 9090             |
| 3 (March)     | 8989             |
| 4 (April)     | 8989             |
| 5 (May)       | 8484             |
| 6 (June)      | 7373             |

### Steps to find the least-squares regression line:
1. **Calculate the means** of x and y.
   \[
   \bar{x} = \frac{1 + 2 + 3 + 4 + 5 + 6}{6}, \quad \bar{y} = \frac{9292 + 9090 + 8989 + 8989 + 8484 + 7373}{6}
   \]

2. **Calculate the slope (m)** using the formula:
   \[
   m = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}}
   \]

3. **Calculate the y-intercept (b)** using the formula:
   \[
   b = \bar{y} - m\bar{x}
   \]

Let me calculate this.The least-squares regression line that models the given data is:

\[
y = -326.09x + 9844.13
\]

This equation can be used to estimate the spending based on the month, where \(x\) is the month number (e.g., \(x = 1\) for January, \(x = 2\) for February, and so on).

Do you have any questions or would you like further details?

Here are 5 related questions:
1. How accurate is this model for predicting future months' spending?
2. What would the predicted spending be for July 2016 using this model?
3. How would changes in spending trends affect the slope of the line?
4. Can the regression line predict when spending might reach zero?
5. How do outliers, if any, affect the accuracy of this regression?

**Tip:** The slope indicates how much spending changes per month. A negative slope means spending is decreasing over time.

The total amount of construction spending on highways and streets​ (in billions of​ dollars) is given in the accompanying table for the first six months of 2016.

Month
January
February
March
April
May
June

Spending
9292
9090
8989
8989
8484
7373
​(a) Find the​ least-squares regression line that models these​ data, with x = 1 corresponding to January 2016.

Find the least-squares regression line for construction spending from January to June 2016. Learn how to calculate the slope and y-intercept of the linear model, understand spending trends, and predict future values. Suitable for high school statistics students.

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