Question

enter values for x and y in the table to plot points in the graph. the table contains data for five students: hours slept, x, and corresponding test scores, y. use the regression calculator to make a scatterplot with a trend line. based on the trend line, what score would you expect after sleeping for 5 hours? as the number of hours sleeping increases, the coressponding test score tends to increase tends to decrease is not affected can not be determined

Explanation:

Step1: Enter data into regression calculator

Input the \(x\) values (\(4\), \(6\), \(6\), \(8\), \(10\)) and \(y\) values (\(62\), \(75\), \(88\), \(79\), \(97\)) into the regression calculator.

Step2: Find the regression equation

Using the calculator, the regression equation (assuming linear regression for simplicity, though other regressions could be considered) is of the form \(y = mx + b\). For this data, after calculation, the equation is approximately \(y=4.8x + 42.8\).

Step3: Predict for \(x = 5\)

Substitute \(x = 5\) into the equation: \(y=4.8\times5+42.8=24 + 42.8=66.8\approx67\).

Step4: Analyze the trend

Looking at the data points (\(x = 4,y = 62\); \(x=6,y = 75\) or \(88\); \(x = 8,y = 79\); \(x = 10,y = 97\)), as \(x\) (hours of sleep) increases, \(y\) (test score) generally has an upward - trend.

Answer:

For the score after sleeping 5 hours: \(67\).
For the trend: tends to increase.