Question

enter values for x and y in the table to plot points in the graph. the table contains data for five students: hours studied, 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 studying for 5 hours? as the number of hours studying increases, the coressponding test score

Explanation:

Step1: Calculate the regression equation

Using a regression calculator (or software like Excel, Google Sheets, or statistical calculators), input the data points \((x_1 = 1,y_1=76)\), \((x_2 = 2,y_2 = 81)\), \((x_3=4,y_3 = 89)\), \((x_4=7,y_4 = 87)\), \((x_5=8,y_5 = 91)\). The general form of a linear regression equation is \(y=ax + b\). After performing the regression calculation (using the formula \(a=\frac{n\sum(xy)-\sum x\sum y}{n\sum(x^{2})-(\sum x)^{2}}\) and \(b=\frac{\sum y - a\sum x}{n}\), where \(n = 5\)), we get \(y\approx2.07x+74.3\)

Step2: Predict the value for \(x = 5\)

Substitute \(x = 5\) into the regression equation \(y=2.07x + 74.3\). Then \(y=2.07\times5+74.3\).

$$y=10.35 + 74.3=84.65\approx85$$

Step3: Analyze the trend

Looking at the data points \((1,76)\), \((2,81)\), \((4,89)\), \((7,87)\), \((8,91)\) and the regression line (which has a positive slope \(a\approx2.07>0\)), as \(x\) (hours of study) increases, \(y\) (test - score) tends to increase.

Answer:

Based on the trend line, the expected score after studying for 5 hours is approximately \(85\). The test score tends to increase as the number of hours studying increases.