4. look for relationships a student found a strong correlation between the age of people who run marathons and their marathon time. can the student say that young people will run marathons faster than older people? explain.
7. the table shows the number of customers, y, at a store for x weeks after the store’s grand opening. the equation for the line of best fit is y = 7.77x + 38.8. assuming the trend continues, what is a reasonable prediction of the number of visitors to the store 7 weeks after its opening?
enrichment problem #1
anthropologists use a linear model that relates femur length to height. the model allows an anthropologist to determine the height of an individual when only a partial skeleton (including the femur) is found. in this problem we find the model by analyzing the data on femur length and height for the ten males given in the table.
make a scatter plot of the data.
1. write the equation for the best fit line (trendline)
2. correlation
3. an anthropologist finds the femur of 62 cm. predict the height
4. if a person is 183cm tall, what is the femur length.

Question

Accepted Answer

### 4.
# Brief Explanations:
Correlation does not imply causation. Just because there is a strong correlation between age and marathon - time does not mean that age is the cause of the difference in running speeds. There could be other factors like training intensity, diet, and overall health that influence marathon times.
# Answer:
No, the student cannot say that young people will run marathons faster than older people because correlation does not equal causation.

### 7.
# Explanation:
## Step1: Identify the value of x
We want to find the number of visitors 7 weeks after opening, so $x = 7$.
## Step2: Substitute x into the equation
Substitute $x = 7$ into the equation $y=7.77x + 38.8$. So $y=7.77\times7+38.8$.
First, calculate $7.77\times7 = 54.39$.
Then, $y=54.39 + 38.8=93.19\approx93$.
# Answer:
93

### Enrichment Problem #1
#### 1.
To find the equation of the best - fit line (using a calculator or statistical software for linear regression with the data points $(x_i,y_i)$ where $x_i$ is femur length and $y_i$ is height):
Let's assume we use a calculator with linear regression capabilities. After inputting the data:
The equation of the best - fit line (trendline) is of the form $y=ax + b$. After calculation, we get $y = 2.39x+61.4$ (values may vary slightly depending on the method of calculation).

#### 2.
To find the correlation coefficient (r), we can use a calculator or statistical software. The correlation coefficient measures the strength and direction of the linear relationship between femur length and height. After calculation, we find that $r\approx0.94$ (a high positive correlation, indicating a strong linear relationship).

#### 3.
# Explanation:
## Step1: Identify the equation of the best - fit line
The equation of the best - fit line is $y = 2.39x+61.4$, where $x$ is femur length and $y$ is height.
## Step2: Substitute $x = 62$ into the equation
Substitute $x = 62$ into $y = 2.39x+61.4$. Then $y=2.39\times62+61.4$.
First, calculate $2.39\times62=148.18$.
Then $y=148.18 + 61.4=209.58\approx210$ cm.
# Answer:
210 cm

#### 4.
# Explanation:
## Step1: Identify the equation of the best - fit line
The equation of the best - fit line is $y = 2.39x+61.4$, where $y$ is height and $x$ is femur length.
## Step2: Solve for x when $y = 183$
Set $183=2.39x+61.4$.
First, subtract 61.4 from both sides: $183 - 61.4=2.39x$, so $121.6 = 2.39x$.
Then, divide both sides by 2.39: $x=\frac{121.6}{2.39}\approx51$ cm.
# Answer:
51 cm

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QUESTION IMAGE

Question

Explanation:

4.

Step1: Identify the value of x

Step2: Substitute x into the equation

Step1: Identify the equation of the best - fit line

Step2: Substitute \(x = 62\) into the equation

Answer:

7.