The data below are the final exam scores of 19 randomly selected history students and the number of hours they slept the night before the exam. Find the equations of the least squares regression line for the given data. Round to the nearest hundredth.
\begin{tabular}{l|c|c|c|c|c|c|c|c|c|c|}
Hours, $\mathrm{x}$ & 3 & 5 & 2 & 8 & 2 & 4 & 4 & 5 & 6 & 3 \\
\hline Scores, $\mathrm{y}$ & 65 & 80 & 60 & 88 & 66 & 78 & 85 & 90 & 90 & 71
\end{tabular}

Step 1 ：We are given the final exam scores of 19 randomly selected history students and the number of hours they slept the night before the exam. We are asked to find the equations of the least squares regression line for the given data.

Step 2 ：The data is as follows: Hours, x: [3, 5, 2, 8, 2, 4, 4, 5, 6, 3] Scores, y: [65, 80, 60, 88, 66, 78, 85, 90, 90, 71]

Step 3 ：To find the equation of the least squares regression line, we need to calculate the slope and the y-intercept.

Step 4 ：The slope (b1) can be calculated using the formula: \(b1 = \frac{\Sigma[(xi - \bar{x})(yi - \bar{y})]}{\Sigma[(xi - \bar{x})^2]}\) where xi and yi are the individual sample points indexed with i, \(\bar{x}\) is the mean of the x values, and \(\bar{y}\) is the mean of the y values.

Step 5 ：The y-intercept (b0) can be calculated using the formula: \(b0 = \bar{y} - b1*\bar{x}\)

Step 6 ：Calculating the mean of x and y values, we get: \(\bar{x} = 4.2\) and \(\bar{y} = 77.3\)

Step 7 ：Substituting these values into the formulas, we get: \(b1 = 5.044303797468355\) and \(b0 = 56.1139240506329\)

Step 8 ：Rounding these values to the nearest hundredth, we get: \(b1 = 5.04\) and \(b0 = 56.11\)

Step 9 ：Substituting these values into the equation of the line, we get the final equation of the least squares regression line: \(y = 5.04x + 56.11\)

Step 10 ：Final Answer: The equation of the least squares regression line for the given data is \(\boxed{y = 5.04x + 56.11}\)