A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21
students who have previously taken the course are given in the table.

Test Scores
Student	First Test Grade	Second Test Grade
1	61
71
2	43
80
3	50
73
4	95
54
5	46
81
6	67
73
7	58
75
8	69
71
9	96
55
10	53
72
11	72
63
12	67
73
13	46
73
14	80
67
15	63
66
16	44
76
17	55
75
18	77
68
19	93
61
20	86
60
21	52
79
Step 1 of 2 :  Using statistical software, estimate the parameters of the model

Second Test Grade=β0+β1(First Test Grade)+εi
.

Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

To estimate the parameters of the model:

\[
\text{Second Test Grade} = \beta_0 + \beta_1 (\text{First Test Grade}) + \epsilon_i
\]

we would typically run a linear regression analysis. The coefficients \(\beta_0\) (intercept) and \(\beta_1\) (slope) are estimated based on the data, where:

- \(\beta_0\) is the intercept, or the expected value of the second test grade when the first test grade is zero.
- \(\beta_1\) is the slope, or the change in the second test grade for a one-unit increase in the first test grade.

Since I do not have access to statistical software right now, I recommend using a software like Excel, Python (using `statsmodels` or `scikit-learn`), R, or any other statistical tool to calculate the regression parameters.

However, if you want me to walk through the steps or if you have access to such software, I can guide you further. Would you like detailed steps for running this regression in a specific tool, or do you want help interpreting the results after you run it?

A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table. Step 1 of 2: Using statistical software, estimate the parameters of the model Second Test Grade=β0+β1(First Test Grade)+εi. Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

Learn how to estimate the parameters of a linear regression model to predict student test scores based on their performance on the first test. This solution involves running regression analysis to estimate the intercept and slope for the equation Second Test Grade = β0 + β1(First Test Grade). Suitable for college and university students studying statistics.

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