Multiple Regression Analysis

Name

Name of Institution

Research question

Are the following statistically significant predictors of a student’s math self-efficacy?

- sex
- number of years math teacher has taught high school math
- belief about usefulness of math in everyday life
- belief that most people can learn to be good at math

Results

The results are presented in the tables below.

Model Summary |
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Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | Change Statistics | ||||

R Square Change | F Change | df1 | df2 | Sig. F Change | |||||

1 | .413^{a} |
.170 | .170 | .91765 | .170 | 726.198 | 4 | 14157 | .000 |

a. Predictors: (Constant), T1 Student’s sex, Years math teacher has taught high school math, Teenager thinks math is useful for everyday life, Most people can learn to be good at math |

ANOVA^{a} |
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Model | Sum of Squares | df | Mean Square | F | Sig. | |

1 | Regression | 2446.067 | 4 | 611.517 | 726.198 | .000^{b} |

Residual | 11921.327 | 14157 | .842 | |||

Total | 14367.394 | 14161 | ||||

a. Dependent Variable: T2 Scale of student’s mathematics self-efficacy | ||||||

b. Predictors: (Constant), T1 Student’s sex, Years math teacher has taught high school math, Teenager thinks math is useful for everyday life, Most people can learn to be good at math |

A total of 14162 cases were analysed in this study. The model summary results show that sex, number of years math teacher has taught high school math, belief about usefulness of math in everyday life, and belief that anybody can learn, and the belief that anybody can learn to be good at math are a statistically significant predictor of a student’s math self-efficacy in students, with R = .170, p < .001. Thus, 17.0% of the variance in self-efficacy is explained by these factors. Further, the ANOVA test confirms that the predictor variables are statistically significant predictors of a student’s self-efficacy for mathematics, with F(4, 14157) = 726.198, p < .001.

Coefficients^{a} |
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Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | 95.0% Confidence Interval for B | |||

B | Std. Error | Beta | Lower Bound | Upper Bound | ||||

1 | (Constant) | -1.855 | .050 | -37.255 | .000 | -1.953 | -1.758 | |

Years math teacher has taught high school math | .004 | .001 | .032 | 4.214 | .000 | .002 | .006 | |

Most people can learn to be good at math | .398 | .012 | .274 | 34.409 | .000 | .375 | .421 | |

Teenager thinks math is useful for everyday life | .308 | .011 | .225 | 28.315 | .000 | .287 | .329 | |

T1 Student’s sex | -.164 | .015 | -.082 | -10.635 | .000 | -.195 | -.134 | |

a. Dependent Variable: T2 Scale of student’s mathematics self-efficacy |

The coefficients table above shows that each of the independent variable is a statistical significant predictor of a student’s math self-efficacy. The model summary is as follows:

Math self-efficacy = -1.855 + 0.004 (years math teacher has taught high school math) + 0.398 (level of belief that most people can learn math) + 0.308 (belief that math is useful for everyday life) – 0.164 (Female)

The model summary shows that for every year increase in the number of years math teacher has taught high school math, we expect 0.004 unit increase in the level of a student’s math self-efficacy. Though the number of years math teacher has taught math in high school is a significant predictor of math self-efficacy, it accounts for a very small positive change. For every increase in the level of belief that most people can learn math, we expect 0.398 unit increase in the level of a student’s math self-efficacy. Similarly, for every increase in the level of belief that math is useful for everyday life, we expect 0.308 unit increase in the level of a student’s math self-efficacy. Finally, being female is associated with 0.164 unit decrease in the level of a student’s math self-efficacy.

These results provide knowledge for improving math self-efficacy among students. First, study shows the need to encourage girls to like math and believe that they can do well in mathematics. Second, it shows that students need to be encouraged that anybody can do well in mathematics so that they can understand that math is not a preserve of a specific group of students. Three, students need to be made to understand that math is useful for their everyday life.

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