Final answer:
The slope of the least squares line is approximately 1.039, and the y-intercept is approximately 2.23, leading to the equation y = 1.039x + 2.23 for the sample of five married couples.
Step-by-step explanation:
The objective is to calculate the slope (m) of the least squares line for a sample of five married couples, where x is the age of the younger partner and y is the age of the older partner. The slope of the least squares line can be computed using the formula m = SSXY / SSX, where SSXY and SSX are given. With SSX = 126.8 and SXY = 131.8, we can calculate m = 131.8 / 126.8 ≈ 1.039 rounded to three decimal places, thus m ≈ 1.039. To find the y-intercept (b), we use the formula b = y⁻ - m * x⁻, where y⁻ and x⁻ are the means of the y and x variables, respectively. Given y⁻ = 31.2 and x⁻ = 27.2, we find b = 31.2 - (1.039 * 27.2) ≈ 2.23. Therefore, the final equation for the least squares line is y = 1.039x + 2.23.