Question

HELP ME PLEASE I FAILED AND HAVE ONE MORE CHANCE!!

Answer 1

The data in the table and the line of best fit equation obtained from the specified data indicates;

Based on the shape of the scatter plot, the best model is; e. Linear

Find the equation of the line of best fit; b. y = -1.01·x + 12.05

Use the equation to predict the value of y when x = 10. d. 1.95

What is a line of best; The line of best fit is the line that best represents the linear relationship between the variables.

Please find attached the graph of the scatter plot which shows a strong negative correlation between the x and y-values, which indicates a linear relationship. Therefore, the best model is a linear model

The equation of the line of best fit, which can be obtained from the least squares regression equation,
`\hat{y}` = a + b·x, where;

The coefficient b is;
`b = \frac{\sum (x - \bar{x})* (y - \bar{y})}{\sum( x - \bar{x})^2}`

`\sum (x - \bar{x})* (y - \bar{y})}` = -42.6

`{\sum( x - \bar{x})^2}` = 42

Therefore, b is; -42.6/42 ≈ -1.01

`\bar{x}` = 3.5

`\bar{y}` = 8.5

Therefore; 8.5 = a + -42.6/42 × 3.5

a = 8.5 + 42.6/42 × 3.5

8.5 + 42.6/42 × 3.5 = 12.05

Therefore, the lease squares regression equation is;
`\hat{y}` = 12.05 - 1.01·x, which corresponds to equation b

The value of f when x = 10, can be found by plugging in the value x = 10 in the equation as follows;

`\hat{y}` = 12.05 - 1.01 × 10

`\hat{y}` = 1.95, which corresponds to option d 1.95