Question

Use the tables to create scatterplots and determine which scatterplot shows a non-linear association.(1 point)
Responses

x
x
50 46 80 59 78 64 68 53 70 68
y
y
90 100 57 80 60 75 72 82 70 67
x 50 46 80 59 78 64 68 53 70 68 y 90 100 57 80 60 75 72 82 70 67

x
x
50 46 80 59 78 64 68 53 70 68
y
y
35 30 75 45 70 50 55 36 62 67
x 50 46 80 59 78 64 68 53 70 68 y 35 30 75 45 70 50 55 36 62 67

x
x
50 46 90 59 78 64 68 53 70 72
y
y
75 71 100 80 90 82 85 77 87 89
x 50 46 90 59 78 64 68 53 70 72 y 75 71 100 80 90 82 85 77 87 89

x
x
50 46 98 59 78 64 68 53 70 72
y
y
75 71 90 55 70 100 90 25 40 76

Answer 1

To determine which scatterplot shows a non-linear association, let's analyze the data sets provided.

1. **First Data Set**:
- x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- y: 90, 100, 57, 80, 60, 75, 72, 82, 70, 67

**Scatterplot Analysis**: This data may display a weak linear trend, but there's a lot of variability, especially on the low end of y-values.

2. **Second Data Set**:
- x: 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
- y: 35, 30, 75, 45, 70, 50, 55, 36, 62, 67

**Scatterplot Analysis**: This data appears to have a somewhat fluctuating pattern, but there is no clear linear association.

3. **Third Data Set**:
- x: 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
- y: 75, 71, 100, 80, 90, 82, 85, 77, 87, 89

**Scatterplot Analysis**: This data set likely demonstrates a clear linear association as y increases consistently with x.

4. **Fourth Data Set**:
- x: 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
- y: 75, 71, 90, 55, 70, 100, 90, 25, 40, 76

**Scatterplot Analysis**: This dataset exhibits non-linear behavior due to variability in y where for lower values of x, y values decrease before increasing again.

Based on the analysis, the **second data set** and **fourth data set** demonstrate non-linear associations, but the **fourth data set** has a more evident non-linear trend due to its varied response at different x-values. Thus, the **fourth dataset** is most likely the scatterplot showing a non-linear association.

Referencing the datasets, you can plot them to visually confirm the non-linear trends. If you'd like, I can also guide you through how to create the plots or any further analysis needed!