Question

part three: linear regression

1. use your calculator to input your fat (x) and calories (y) information for each find the equation of the line of best fit: y = mx + b

equation: y = 12.97x+1163

1. find the correlation coefficient (r): 0.981
2. interpret the correlation: is it strong, weak, positive, negative, or none? explain.
3. what does the slope mean in the context of fast food items?
4. predict: use your equation above to predict the number of calories in a sandwich with 14 grams of fat. show your work.

part four: put your learning into words!
in a minimum of 5 sentences, summarize what you learned about linear regression in terms of correlation, “r” values, and trend lines. use good mathematical vocab.

Explanation:

Step1: Identify correlation coefficient interpretation

The correlation coefficient \(r\) values range from - 1 to 1. If \(r\) is close to 1, it's a strong positive correlation; close to - 1, strong negative; close to 0, weak.

Step2: Interpret given \(r = 0.941\)

Since \(r=0.941\) which is close to 1, it is a strong positive correlation. This means as the amount of fat in fast - food items increases, the number of calories also tends to increase significantly.

Step3: Interpret slope meaning

The slope \(m = 12.97\) in the equation \(y=mx + b\) (where \(y\) is calories and \(x\) is fat) means that for every additional gram of fat in a fast - food item, the number of calories increases by approximately 12.97.

Step4: Predict calories for 14 grams of fat

Substitute \(x = 14\) into the equation \(y=12.97x+116.3\).
\[y=12.97\times14 + 116.3\]
\[y = 181.58+116.3\]
\[y=297.88\]

Answer:

1. The correlation is strong and positive because the correlation coefficient \(r = 0.941\) is close to 1, indicating that as the fat content in fast - food items increases, the calorie content also increases significantly.
2. The slope of 12.97 means that for each additional gram of fat in a fast - food item, the number of calories increases by approximately 12.97.
3. The predicted number of calories in a sandwich with 14 grams of fat is 297.88.