The graph shows the number of hours per day spent on social media by a group of teenagers and the number of hours per day spent exercising. A line of best fit for the data is shown.
A scatterplot is shown in the xy-plane. The horizontal axis is labeled as Social Media Hours Per Day and the vertical axis is labeled as Exercising Hours Per Day. The values on the horizontal axis range from 0 to 1.6 in increments of 0.2 and the values on the y-axis range from 0 to 2 in increments of 0.2. The line of best fit intersects the x-axis at a point just to the left of 1 decimal point 4 and y-axis at a point just below 1.1. Majority of the data points are concentrated between 0.3 and 0.6 on the horizontal axis and 0.6 and 0.9 on the vertical axis and two points are marked on the line.
Use the graph to determine how many hours a teenager would spend exercising in one day if they spent 0.25 hours on social media.
Use the graph to determine how many hours a teenager would spend exercising in one day if they spent 1.38 hours on social media.
Do you think the predictions from part (a) and part (b) are reliable? Explain your reasoning.
a. 1.7 hours of exercise
b. 1.1 hours of exercise
c. no, there just estimates each teen is different
To determine the number of hours a teenager would spend exercising if they spent 0.25 hours on social media, we can locate the point on the line of best fit that corresponds to the x-value of 0.25. In this case, since the line of best fit intersects the x-axis just to the left of 1.4, we can estimate that the corresponding y-value would be just below 1.1.
To determine the number of hours a teenager would spend exercising if they spent 1.38 hours on social media, we can use the same approach. Based on the position of the line of best fit, we can estimate that the corresponding y-value would be around 0.6.
Regarding the reliability of the predictions:
For part (a) where the x-value is 0.25, the y-value is estimated to be just below 1.1. This prediction is within the range of the majority of data points concentrated between 0.6 and 0.9 on the vertical axis. Therefore, this prediction appears to be reliable.
For part (b) where the x-value is 1.38, the y-value is estimated to be around 0.6. However, based on the concentration of data points between 0.3 and 0.6 on the horizontal axis, it appears that the line of best fit might not accurately represent the relationship between social media hours and exercising hours for values greater than 1. In this case, the prediction may not be as reliable.
In summary, the prediction in part (a) seems reliable based on the distribution of data, but the prediction in part (b) may be less reliable due to the potential limitations of the line of best fit for values greater than 1.
To determine how many hours a teenager would spend exercising in one day if they spent 0.25 hours on social media based on the graph, we need to find the corresponding value on the y-axis (exercising hours).
1. Locate the value 0.25 on the horizontal axis (Social Media Hours Per Day).
2. Move vertically from that point until you intersect the line of best fit.
3. From the intersection point on the line of best fit, move horizontally to the y-axis (Exercising Hours Per Day).
4. Read the value on the y-axis to determine the number of hours a teenager would spend exercising.
To determine how many hours a teenager would spend exercising in one day if they spent 1.38 hours on social media using the graph, follow the same steps as before:
1. Locate the value 1.38 on the horizontal axis (Social Media Hours Per Day).
2. Move vertically from that point until you intersect the line of best fit.
3. From the intersection point on the line of best fit, move horizontally to the y-axis (Exercising Hours Per Day).
4. Read the value on the y-axis to determine the number of hours a teenager would spend exercising.
Based on the graph, it appears that for 0.25 hours on social media, a teenager would spend around 0.94 hours exercising. For 1.38 hours on social media, a teenager would spend approximately 0.46 hours exercising.
As for the reliability of these predictions, it depends on certain factors. The line of best fit is drawn based on the given data points, and it provides an estimate or trend for the relationship between social media and exercise. However, the predictions may not be entirely reliable for several reasons:
1. Outliers or missing data: The line of best fit assumes a linear relationship between the variables, but there may be individual cases that deviate significantly from the trend. Missing or incomplete data could also affect the reliability of the predictions.
2. Nonlinear relationship: The data points may not follow a strictly linear relationship. In this case, the line of best fit may not accurately capture the true trend, and its predictions may be less reliable.
3. Limited range of data: The concentration of data points within a specific range (0.3 to 0.6 on the x-axis and 0.6 to 0.9 on the y-axis) suggests that the predictions within that range may be more reliable. However, predictions outside this range may have higher uncertainty.
Therefore, while the line of best fit provides a general trend, it may not accurately predict individual cases with certainty. It's important to consider other relevant factors and gather additional data to make more reliable predictions.