Question
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
The y-intercept is 41.16. The machine starts with 41.16 ounces of diet soda.
The y-intercept is 41.16. The machine loses about 41.16 fluid ounces of diet soda each hour.
The y-intercept is −4.5. The machine starts with 4.5 ounces of diet soda.
The y-intercept is −4.5. The machine loses about 4.5 fluid ounces of diet soda each hour.
The y-intercept is 41.16. The machine starts with 41.16 ounces of diet soda.
The y-intercept is 41.16. The machine loses about 41.16 fluid ounces of diet soda each hour.
The y-intercept is −4.5. The machine starts with 4.5 ounces of diet soda.
The y-intercept is −4.5. The machine loses about 4.5 fluid ounces of diet soda each hour.
Answers
Answered by
GPT-4o mini
Given that we need to find the y-intercept of the line of fit and explain its meaning in context, we'll analyze the provided options.
1. The first option suggests that the y-intercept is 41.16 and indicates that the machine starts with 41.16 ounces of diet soda.
2. The second option also states that the y-intercept is 41.16 but claims that the machine loses about 41.16 fluid ounces of diet soda each hour.
3. The third option identifies the y-intercept as -4.5 and suggests that the machine starts with 4.5 ounces of diet soda.
4. The fourth option again states the y-intercept is -4.5 but says the machine loses about 4.5 fluid ounces of diet soda each hour.
To interpret the y-intercept meaningfully:
- The y-intercept (in context of the line of fit) typically indicates the starting value of the dependent variable when the independent variable is zero. If we consider the equation of a line in a linear regression (often in the form \(y = mx + b\), where \(b\) is the y-intercept), this means that it provides insight into the situation at the initial point of measurement.
### Explanation in Context:
- If the y-intercept is **41.16**, this suggests that when measurements begin (at hour zero), the machine contains **41.16 ounces of diet soda**. This might indicate a starting condition or inventory level before any loss occurs.
- If the y-intercept were **-4.5**, it would imply that at hour zero, there would be a negative amount of diet soda, which does not make practical sense in this scenario, as we can't have a negative quantity for physical content like diet soda.
Thus, from the options you presented:
- The correct interpretation regarding a realistic starting point would be the first option: **The y-intercept is 41.16. The machine starts with 41.16 ounces of diet soda.**
This choice correctly states that at the beginning of observation, the machine began with 41.16 ounces, which is a meaningful result in the context of the data being analyzed.
1. The first option suggests that the y-intercept is 41.16 and indicates that the machine starts with 41.16 ounces of diet soda.
2. The second option also states that the y-intercept is 41.16 but claims that the machine loses about 41.16 fluid ounces of diet soda each hour.
3. The third option identifies the y-intercept as -4.5 and suggests that the machine starts with 4.5 ounces of diet soda.
4. The fourth option again states the y-intercept is -4.5 but says the machine loses about 4.5 fluid ounces of diet soda each hour.
To interpret the y-intercept meaningfully:
- The y-intercept (in context of the line of fit) typically indicates the starting value of the dependent variable when the independent variable is zero. If we consider the equation of a line in a linear regression (often in the form \(y = mx + b\), where \(b\) is the y-intercept), this means that it provides insight into the situation at the initial point of measurement.
### Explanation in Context:
- If the y-intercept is **41.16**, this suggests that when measurements begin (at hour zero), the machine contains **41.16 ounces of diet soda**. This might indicate a starting condition or inventory level before any loss occurs.
- If the y-intercept were **-4.5**, it would imply that at hour zero, there would be a negative amount of diet soda, which does not make practical sense in this scenario, as we can't have a negative quantity for physical content like diet soda.
Thus, from the options you presented:
- The correct interpretation regarding a realistic starting point would be the first option: **The y-intercept is 41.16. The machine starts with 41.16 ounces of diet soda.**
This choice correctly states that at the beginning of observation, the machine began with 41.16 ounces, which is a meaningful result in the context of the data being analyzed.
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