Answer:
Therefore, the approximate value of y for x = 4 is approximately 0.97.
Step-by-step explanation:
To determine the approximate value of y for x = 4, we need to use the values in the table to find a mathematical relationship between x and y. This can be done by performing a linear regression analysis on the data.A linear regression model is a statistical model that represents the relationship between two variables as a linear equation. The equation of the line is given by:y = mx + bWhere m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).We can use the values in the table to calculate the values of m and b. Using the formula for the slope of a line:m = (Σ(xy) - (Σx)(Σy)/n) / (Σ(x^2) - (Σx)^2/n)Where Σ(xy) is the sum of the products of the x and y values, Σx is the sum of the x values, Σy is the sum of the y values, Σ(x^2) is the sum of the squares of the x values, and n is the number of data points.Plugging in the values from the table, we get:m = (1146.07 - (69.7)(625.99)/5) / (1152.64 - (69.7)^2/5)m = 0.68The y-intercept can be calculated using the formula:b = (Σy - m(Σx)) / nPlugging in the values from the table and the value of m that we just calculated, we get:b = (625.99 - 0.68(69.7)) / 5b = -1.75We can now use the values of m and b to write the equation of the line:y = 0.68x - 1.75To determine the approximate value of y for x = 4, we can substitute this value into the equation:y = 0.68 * 4 - 1.75y = 2.72 - 1.75y = 0.97