The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a best-fitting linear model that express Vitamin C content as a function of the weight of the Raspberries.

Grams: 55, 60, 65, 70, 75, 80, 85 

Vitamin C content in mg: 11.8, 14.3, 16.1, 18.1, 20.3, 23, 25.8

A) find the regression equation: y= _____x + ______ round to the nearest 3 decimal places 

B) If we test 115 grams of raspberries what is the expected vitamin C content? _____mg round to one place as needed 

To find the best-fitting linear model (regression equation) for the data, we need to perform linear regression. The general form of a linear equation is:

\[
y = mx + b
\]

Where:
- \( y \) is the Vitamin C content in mg.
- \( x \) is the weight of the raspberries in grams.
- \( m \) is the slope of the line.
- \( b \) is the y-intercept.

### Given Data:
- Grams of raspberries (\( x \)): 55, 60, 65, 70, 75, 80, 85
- Vitamin C content (\( y \)): 11.8, 14.3, 16.1, 18.1, 20.3, 23, 25.8

I'll calculate the slope (\( m \)) and the intercept (\( b \)) using the formula for linear regression, and then find the expected Vitamin C content for 115 grams of raspberries.

Let me calculate this.### A) The regression equation is:

\[
y = 0.454x - 13.314
\]

Where \( y \) is the Vitamin C content in mg, and \( x \) is the weight of the raspberries in grams.

### B) If we test 115 grams of raspberries, the expected Vitamin C content is:

\[
38.9 \, \text{mg}
\]

Would you like to explore the details of this calculation or have any other questions?

### Related Questions:
1. How do we interpret the slope and intercept in this context?
2. What is the significance of the \( R^2 \) value in linear regression?
3. Could we use this model to predict Vitamin C content for very small or very large weights of raspberries?
4. How can the residuals of this model help evaluate its accuracy?
5. What are the potential sources of error in such a regression model?

### Tip:
In regression, always check the goodness-of-fit (e.g., \( R^2 \) value) to assess how well the model explains the data.

The table below shows data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a best-fitting linear model that expresses Vitamin C content as a function of the weight of the Raspberries.

Grams: 55, 60, 65, 70, 75, 80, 85
Vitamin C content in mg: 11.8, 14.3, 16.1, 18.1, 20.3, 23, 25.8

A) Find the regression equation: y= _____x + ______ round to the nearest 3 decimal places

B) If we test 115 grams of raspberries what is the expected vitamin C content? _____mg round to one place as needed.

Learn how to find the best-fitting linear model for predicting Vitamin C content based on raspberry weight. This problem uses linear regression, analyzing data points such as 55g to 85g of raspberries with corresponding Vitamin C content. The step-by-step solution includes finding the regression equation and predicting Vitamin C for 115g of raspberries.

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