Question

To minimize the negative impact of math anxiety on achievement in a research design course, a group of researchers implemented a series of feedback sessions, in which the teacher went over the small-group assignments and discussed the most frequently committed errors. At the end of the course, data from 166 students were obtained. The researchers investigated how students' final exam scores were explained by math course anxiety, math test anxiety, numerical task anxiety, enjoyment, self-confidence, motivation, and perceived usefulness of the feedback sessions. (a) What is the response variable? (b) What are the units, and the number of units, n? (c) What are the explanatory variables? (d) The following table contains the estimated coefficients and standard errors of their multiple regression fit. Each explanatory variable is an average five-point Likert scale questions. | Variable | Estimate | SE | | :--- | :--- | :--- | | Intercept | 1.316 | 0.65 | | Math course anxiety | -0.212 | 0.11 | | Math test anxiety | -0.155 | 0.12 | | Numerical task anxiety | -0.094 | 0.12 | | Enjoyment | 0.176 | 0.11 | | Self-confidence | 0.118 | 0.11 | | Motivation | 0.097 | 0.12 | | Feedback usefulness | 0.644 | 0.19 | (e) Look at the signs of the coefficients (positive and negative). Is this what you would expect in this setting? Explain. (f) What are the degrees of freedom for the model and error? (g) Test the significance of each coefficient (i.e., test if the coefficient significantly different from zero?) and state your conclusions. Calculate 95% CI for each coefficient. (h) Redo the significance tests in (g) after correcting for multiplicity using the BH procedure.

          To minimize the negative impact of math anxiety on achievement in a research design
course, a group of researchers implemented a series of feedback sessions, in which
the teacher went over the small-group assignments and discussed the most frequently
committed errors. At the end of the course, data from 166 students were obtained.
The researchers investigated how students' final exam scores were explained by math
course anxiety, math test anxiety, numerical task anxiety, enjoyment, self-confidence,
motivation, and perceived usefulness of the feedback sessions.

(a) What is the response variable?
(b) What are the units, and the number of units, n?
(c) What are the explanatory variables?
(d) The following table contains the estimated coefficients and standard errors of their
multiple regression fit. Each explanatory variable is an average five-point Likert
scale questions.

| Variable | Estimate | SE |
| :--- | :--- | :--- |
| Intercept | 1.316 | 0.65 |
| Math course anxiety | -0.212 | 0.11 |
| Math test anxiety | -0.155 | 0.12 |
| Numerical task anxiety | -0.094 | 0.12 |
| Enjoyment | 0.176 | 0.11 |
| Self-confidence | 0.118 | 0.11 |
| Motivation | 0.097 | 0.12 |
| Feedback usefulness | 0.644 | 0.19 |

(e) Look at the signs of the coefficients (positive and negative). Is this what you
would expect in this setting? Explain.
(f) What are the degrees of freedom for the model and error?
(g) Test the significance of each coefficient (i.e., test if the coefficient significantly
different from zero?) and state your conclusions. Calculate 95% CI for each
coefficient.
(h) Redo the significance tests in (g) after correcting for multiplicity using the BH
procedure.

To minimize the negative impact of math anxiety on achievement in a research design
course, a group of researchers implemented a series of feedback sessions, in which
the teacher went over the small-group assignments and discussed the most frequently
committed errors. At the end of the course, data from 166 students were obtained.
The researchers investigated how students' final exam scores were explained by math
course anxiety, math test anxiety, numerical task anxiety, enjoyment, self-confidence,
motivation, and perceived usefulness of the feedback sessions.

(a) What is the response variable?
(b) What are the units, and the number of units, n?
(c) What are the explanatory variables?
(d) The following table contains the estimated coefficients and standard errors of their
multiple regression fit. Each explanatory variable is an average five-point Likert
scale questions.

| Variable | Estimate | SE |
| :— | :— | :— |
| Intercept | 1.316 | 0.65 |
| Math course anxiety | -0.212 | 0.11 |
| Math test anxiety | -0.155 | 0.12 |
| Numerical task anxiety | -0.094 | 0.12 |
| Enjoyment | 0.176 | 0.11 |
| Self-confidence | 0.118 | 0.11 |
| Motivation | 0.097 | 0.12 |
| Feedback usefulness | 0.644 | 0.19 |

(e) Look at the signs of the coefficients (positive and negative). Is this what you
would expect in this setting? Explain.
(f) What are the degrees of freedom for the model and error?
(g) Test the significance of each coefficient (i.e., test if the coefficient significantly
different from zero?) and state your conclusions. Calculate 95% CI for each
coefficient.
(h) Redo the significance tests in (g) after correcting for multiplicity using the BH
procedure.

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