Question

A random sample of 9 history students produced the following data,

first test Score, x	second test Score, y
12	38
23	36
41	19
66	66
35	40
17	44
72	40
19	72
30	78

where x measures the first test score and y measures the second test score. What is the estimate of the y = a x + b regression intercept coefficient?

Answer 1

we will solve this problem with the help of excel

We know that x denote first test score and y denote second test score

Now steps to get the linear regression equation

1)1st we name two columns x and y then we input the values of x & y

2)we select the column of x and y

3) Go to "INSERT" menu then select the Scatter plot from the chart menu.

4) Now from the scatter plot menu select the 1st one the simple scatter plot

5) Here we get a scatter plot now beside the scatter plot we see a add option known as chart elements we select that

6) Now we select the option "Trendline" and then select the arrow beside Trendline

7)Then we get a few options and we select "More Options"

8) We get options under trendline option which is set to linear by default from there we select the option "Display Equation on chart"

9) We get scatter plot with trendline and linear regression equation.

Output:

Here we don't need the scatter plot but we need the linear regression equation.

The equation we get is y = 48.111

The line is in the form y = a x + b

So,

a = 0 (slope)

b = 48.111 (intercept)

The estimate of the regression intercept coefficient (b) is 48.111