On graph points (1,60),(1,70), (2,70), (2.5,75), (3,75), (3,80), (3.5,80),(4,85), (4.5,90), (5,90) which of the following is an appropriate regression model given the bivariate dataset

Question

f(x) ~ -9x
f(x)~ 9 x
f(x)~ -9x + 10
f(x)~ 9x + 10

Answer 1

To determine the most appropriate regression model from the options provided for the given bivariate dataset, let's analyze the dataset points:

1. (1, 60)
2. (1, 70)
3. (2, 70)
4. (2.5, 75)
5. (3, 75)
6. (3, 80)
7. (3.5, 80)
8. (4, 85)
9. (4.5, 90)
10. (5, 90)

Observations:

• The x-values range from 1 to 5.
• The y-values tend to increase as x increases, suggesting a positive relationship.

Evaluating the Models:

1. f(x) ~ -9x

• This predicts a strong negative relationship, which is contradicted by the data that shows a positive trend.

2. f(x) ~ 9x

• This suggests a strong positive relationship which could fit the increasing trend but does not account for the y-intercept.

3. f(x) ~ -9x + 10

• This also predicts a negative linear relationship, again contrary to the observed data.

4. f(x) ~ 9x + 10

• This suggests a positive linear relationship with a y-intercept of 10. Given the increasing trend in y-values, this model seems plausible.

Conclusion:

Among the choices, f(x) ~ 9x + 10 is the most appropriate regression model considering the observed increasing trend in the dataset. It captures the positive relationship effectively, while the other options suggest negative relationships or do not account for the intercept properly.