Find a regression relating steam usage to temperature. Test for significance of regression using a=0.05. Find a 99% confidence interval for ß1

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**Transcription for Educational Website:**

Title: Analyzing Steam Usage in Relation to Ambient Temperature

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The quantity of steam used each month by a chemical plant appears to be linked to the average ambient temperature (in °F) for that month. The table below presents data from the past year, detailing usage and temperatures.

**Objectives:**

(a) Develop a regression model to relate steam usage to temperature.

(b) Test the regression model's significance using a significance level (α) of 0.05.

(c) Determine a 99% confidence interval for the regression coefficient (β₁).

**Data Table:**

| Month | Temp. (°F) | Usage/1000 |
|-------|------------|------------|
| Jan.  | 21         | 185.79     |
| Feb.  | 24         | 214.47     |
| Mar.  | 32         | 288.03     |
| Apr.  | 47         | 424.84     |
| May   | 50         | 454.58     |
| June  | 59         | 539.03     |
| July  | 68         | 621.55     |
| Aug.  | 74         | 675.06     |
| Sept. | 62         | 562.03     |
| Oct.  | 50         | 452.93     |
| Nov.  | 41         | 315.98     |
| Dec.  | 30         | 273.98     |

**Diagram/Graph Explanation:**

The table is organized into three columns: "Month," "Temp." for the temperature in Fahrenheit, and "Usage/1000," representing the amount of steam used in thousands of pounds. This data is essential for understanding how steam usage correlates with changes in temperature throughout the year.

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End of content for the educational website.
Transcribed Image Text:**Transcription for Educational Website:** Title: Analyzing Steam Usage in Relation to Ambient Temperature --- The quantity of steam used each month by a chemical plant appears to be linked to the average ambient temperature (in °F) for that month. The table below presents data from the past year, detailing usage and temperatures. **Objectives:** (a) Develop a regression model to relate steam usage to temperature. (b) Test the regression model's significance using a significance level (α) of 0.05. (c) Determine a 99% confidence interval for the regression coefficient (β₁). **Data Table:** | Month | Temp. (°F) | Usage/1000 | |-------|------------|------------| | Jan. | 21 | 185.79 | | Feb. | 24 | 214.47 | | Mar. | 32 | 288.03 | | Apr. | 47 | 424.84 | | May | 50 | 454.58 | | June | 59 | 539.03 | | July | 68 | 621.55 | | Aug. | 74 | 675.06 | | Sept. | 62 | 562.03 | | Oct. | 50 | 452.93 | | Nov. | 41 | 315.98 | | Dec. | 30 | 273.98 | **Diagram/Graph Explanation:** The table is organized into three columns: "Month," "Temp." for the temperature in Fahrenheit, and "Usage/1000," representing the amount of steam used in thousands of pounds. This data is essential for understanding how steam usage correlates with changes in temperature throughout the year. --- End of content for the educational website.
Expert Solution
Step 1

Given information:

Given is the bivariate data corresponding to two variables independent one is X (Temperature) and dependent one is Y(Usage).

it is required to find regression line of Y on X. and then test its significance.

 

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