1 Purpose

This R Markdown file reads TrimmedMay27.csv, reproduces the simple Excel-style regressions, and tests the slope parameter one regression at a time.

For each outcome and each predictor, the fitted model is

\[ y_i = \beta_0 + \beta_1 x_i + \varepsilon_i, \]

and the two-sided slope test is

\[ H_0: \beta_1 = 0 \quad\text{versus}\quad H_A: \beta_1 \ne 0. \]

This version does not use the old multi-panel command par(mfrow = c(length(outcomes), length(predictors))) for the main figures. Instead, it generates, displays, and saves every regression plot as a separate PNG file. This keeps the titles, axis labels, equations, and test summaries readable.

2 Read and clean the CSV

## CSV used: TrimmedMay27.csv
## Rows read: 140
## Columns used in the regression analysis: 15

3 Functions for regression, slope tests, equations, and plotting

4 All slope tests with regression equations

The table below is produced by the requested workflow:

results <- make_results_table(dat, outcomes, predictors, alpha = params$alpha)
emit_table(results)

The output includes one regression equation for each outcome-predictor pair.

Target variable Variable names and statistics of slope
Cumulative Score (max 36) log like/view: Predicted Cumulative Score (max 36) = 17.5569 - 3.2141 * log like/view
slope = -3.2141; SE = ; t(131) = -2.0207; p = 0.0454 *; n = 133; R^2 = 0.0302; direction: Negative(Significant)
Technical correctness log like/view: Predicted Technical correctness = 2.4037 - 0.1688 * log like/view
slope = -0.1688; SE = ; t(131) = -1.4598; p = 0.1468 ; n = 133; R^2 = 0.0160; direction: Negative(Not Significant)
Technical completeness log like/view: Predicted Technical completeness = 2.3576 - 0.0247 * log like/view
slope = -0.0247; SE = ; t(131) = -0.1488; p = 0.8819 ; n = 133; R^2 = 0.0002; direction: Negative(Not Significant)
Relevance to learners log like/view: Predicted Relevance to learners = 0.8418 - 0.4446 * log like/view
slope = -0.4446; SE = ; t(131) = -1.5315; p = 0.1281 ; n = 133; R^2 = 0.0176; direction: Negative(Not Significant)
Linking to prior knowledge log like/view: Predicted Linking to prior knowledge = 1.3211 - 0.2498 * log like/view
slope = -0.2498; SE = ; t(131) = -1.2064; p = 0.2298 ; n = 133; R^2 = 0.0110; direction: Negative(Not Significant)
Active engagement log like/view: Predicted Active engagement = 0.3504 + 0.0795 * log like/view
slope = 0.0795; SE = ; t(131) = 0.4017; p = 0.6886 ; n = 133; R^2 = 0.0012; direction: Positive(Not Significant)
Direct addressing log like/view: Predicted Direct addressing = 0.6561 - 0.5893 * log like/view
slope = -0.5893; SE = ; t(131) = -2.2581; p = 0.0256 *; n = 133; R^2 = 0.0375; direction: Negative(Significant)
Use of examples log like/view: Predicted Use of examples = 1.5660 - 0.2178 * log like/view
slope = -0.2178; SE = ; t(131) = -0.9566; p = 0.3405 ; n = 133; R^2 = 0.0069; direction: Negative(Not Significant)
Design of visualizations log like/view: Predicted Design of visualizations = 1.5079 - 0.2085 * log like/view
slope = -0.2085; SE = ; t(131) = -1.0048; p = 0.3168 ; n = 133; R^2 = 0.0076; direction: Negative(Not Significant)
Matching visualizations-text log like/view: Predicted Matching visualizations-text = 1.6491 - 0.3904 * log like/view
slope = -0.3904; SE = ; t(131) = -2.0397; p = 0.0434 *; n = 133; R^2 = 0.0308; direction: Negative(Significant)
Language is comprehensive log like/view: Predicted Language is comprehensive = 1.7527 - 0.5278 * log like/view
slope = -0.5278; SE = ; t(131) = -3.3028; p = 0.0012 **; n = 133; R^2 = 0.0769; direction: Negative(Significant)
Language is precise log like/view: Predicted Language is precise = 1.8163 - 0.3651 * log like/view
slope = -0.3651; SE = ; t(131) = -1.6139; p = 0.1090 ; n = 133; R^2 = 0.0195; direction: Negative(Not Significant)
Coherent overall structure log like/view: Predicted Coherent overall structure = 2.5375 + 0.1857 * log like/view
slope = 0.1857; SE = ; t(131) = 1.0339; p = 0.3031 ; n = 133; R^2 = 0.0081; direction: Positive(Not Significant)
Cumulative Score (max 36) log com/viw: Predicted Cumulative Score (max 36) = 18.0584 - 1.7258 * log com/view
slope = -1.7258; SE = ; t(123) = -2.0611; p = 0.0414 *; n = 125; R^2 = 0.0334; direction: Negative(Significant)
Technical correctness log com/viw: Predicted Technical correctness = 2.5553 - 0.0486 * log com/view
slope = -0.0486; SE = ; t(123) = -0.7172; p = 0.4746 ; n = 125; R^2 = 0.0042; direction: Negative(Not Significant)
Technical completeness log com/viw: Predicted Technical completeness = 1.8791 - 0.1607 * log com/view
slope = -0.1607; SE = ; t(123) = -1.7188; p = 0.0882 .; n = 125; R^2 = 0.0235; direction: Negative(Not Significant)
Relevance to learners log com/viw: Predicted Relevance to learners = 1.3709 - 0.0974 * log com/view
slope = -0.0974; SE = ; t(123) = -0.5856; p = 0.5592 ; n = 125; R^2 = 0.0028; direction: Negative(Not Significant)
Linking to prior knowledge log com/viw: Predicted Linking to prior knowledge = 1.1415 - 0.2076 * log com/view
slope = -0.2076; SE = ; t(123) = -1.7709; p = 0.0791 .; n = 125; R^2 = 0.0249; direction: Negative(Not Significant)
Active engagement log com/viw: Predicted Active engagement = -0.0076 - 0.0659 * log com/view
slope = -0.0659; SE = ; t(123) = -0.5347; p = 0.5939 ; n = 125; R^2 = 0.0023; direction: Negative(Not Significant)
Direct addressing log com/viw: Predicted Direct addressing = 1.9190 + 0.0414 * log com/view
slope = 0.0414; SE = ; t(123) = 0.2622; p = 0.7936 ; n = 125; R^2 = 0.0006; direction: Positive(Not Significant)
Use of examples log com/viw: Predicted Use of examples = 1.6728 - 0.0926 * log com/view
slope = -0.0926; SE = ; t(123) = -0.6986; p = 0.4861 ; n = 125; R^2 = 0.0040; direction: Negative(Not Significant)
Design of visualizations log com/viw: Predicted Design of visualizations = 1.5171 - 0.1243 * log com/view
slope = -0.1243; SE = ; t(123) = -1.0293; p = 0.3054 ; n = 125; R^2 = 0.0085; direction: Negative(Not Significant)
Matching visualizations-text log com/viw: Predicted Matching visualizations-text = 1.7584 - 0.1986 * log com/view
slope = -0.1986; SE = ; t(123) = -1.9176; p = 0.0575 .; n = 125; R^2 = 0.0290; direction: Negative(Not Significant)
Language is comprehensive log com/viw: Predicted Language is comprehensive = 1.6861 - 0.3206 * log com/view
slope = -0.3206; SE = ; t(123) = -4.0357; p = <0.001 ***; n = 125; R^2 = 0.1169; direction: Negative(Significant)
Language is precise log com/viw: Predicted Language is precise = 1.5674 - 0.2825 * log com/view
slope = -0.2825; SE = ; t(123) = -2.3253; p = 0.0217 *; n = 125; R^2 = 0.0421; direction: Negative(Significant)
Coherent overall structure log com/viw: Predicted Coherent overall structure = 1.9384 - 0.0834 * log com/view
slope = -0.0834; SE = ; t(123) = -0.8750; p = 0.3833 ; n = 125; R^2 = 0.0062; direction: Negative(Not Significant)

5 One-by-one downloadable plots and one-by-one slope tests

Each subsection below gives one regression equation, one slope test, and one downloadable PNG plot. The PNG files are written to the folder specified by params$plot_dir.

5.1 Cumulative Score (max 36) against log like/view

Regression equation: Predicted Cumulative Score (max 36) = 17.5569 - 3.2141 * log like/view
Slope test: slope = -3.2141, t(131) = -2.021, p = 0.0454; the slope is statistically significant at alpha = 0.050.

Download this PNG

5.2 Technical correctness against log like/view

Regression equation: Predicted Technical correctness = 2.4037 - 0.1688 * log like/view
Slope test: slope = -0.1688, t(131) = -1.460, p = 0.1468; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.3 Technical completeness against log like/view

Regression equation: Predicted Technical completeness = 2.3576 - 0.0247 * log like/view
Slope test: slope = -0.0247, t(131) = -0.149, p = 0.8819; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.4 Relevance to learners against log like/view

Regression equation: Predicted Relevance to learners = 0.8418 - 0.4446 * log like/view
Slope test: slope = -0.4446, t(131) = -1.532, p = 0.1281; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.5 Linking to prior knowledge against log like/view

Regression equation: Predicted Linking to prior knowledge = 1.3211 - 0.2498 * log like/view
Slope test: slope = -0.2498, t(131) = -1.206, p = 0.2298; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.6 Active engagement against log like/view

Regression equation: Predicted Active engagement = 0.3504 + 0.0795 * log like/view
Slope test: slope = 0.0795, t(131) = 0.402, p = 0.6886; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.7 Direct addressing against log like/view

Regression equation: Predicted Direct addressing = 0.6561 - 0.5893 * log like/view
Slope test: slope = -0.5893, t(131) = -2.258, p = 0.0256; the slope is statistically significant at alpha = 0.050.

Download this PNG

5.8 Use of examples against log like/view

Regression equation: Predicted Use of examples = 1.5660 - 0.2178 * log like/view
Slope test: slope = -0.2178, t(131) = -0.957, p = 0.3405; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.9 Design of visualizations against log like/view

Regression equation: Predicted Design of visualizations = 1.5079 - 0.2085 * log like/view
Slope test: slope = -0.2085, t(131) = -1.005, p = 0.3168; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.10 Matching visualizations-text against log like/view

Regression equation: Predicted Matching visualizations-text = 1.6491 - 0.3904 * log like/view
Slope test: slope = -0.3904, t(131) = -2.040, p = 0.0434; the slope is statistically significant at alpha = 0.050.

Download this PNG

5.11 Language is comprehensive against log like/view

Regression equation: Predicted Language is comprehensive = 1.7527 - 0.5278 * log like/view
Slope test: slope = -0.5278, t(131) = -3.303, p = 0.0012; the slope is statistically significant at alpha = 0.050.

Download this PNG

5.12 Language is precise against log like/view

Regression equation: Predicted Language is precise = 1.8163 - 0.3651 * log like/view
Slope test: slope = -0.3651, t(131) = -1.614, p = 0.1090; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.13 Coherent overall structure against log like/view

Regression equation: Predicted Coherent overall structure = 2.5375 + 0.1857 * log like/view
Slope test: slope = 0.1857, t(131) = 1.034, p = 0.3031; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.14 Cumulative Score (max 36) against log com/view

Regression equation: Predicted Cumulative Score (max 36) = 18.0584 - 1.7258 * log com/view
Slope test: slope = -1.7258, t(123) = -2.061, p = 0.0414; the slope is statistically significant at alpha = 0.050.

Download this PNG

5.15 Technical correctness against log com/view

Regression equation: Predicted Technical correctness = 2.5553 - 0.0486 * log com/view
Slope test: slope = -0.0486, t(123) = -0.717, p = 0.4746; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.16 Technical completeness against log com/view

Regression equation: Predicted Technical completeness = 1.8791 - 0.1607 * log com/view
Slope test: slope = -0.1607, t(123) = -1.719, p = 0.0882; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.17 Relevance to learners against log com/view

Regression equation: Predicted Relevance to learners = 1.3709 - 0.0974 * log com/view
Slope test: slope = -0.0974, t(123) = -0.586, p = 0.5592; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.18 Linking to prior knowledge against log com/view

Regression equation: Predicted Linking to prior knowledge = 1.1415 - 0.2076 * log com/view
Slope test: slope = -0.2076, t(123) = -1.771, p = 0.0791; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.19 Active engagement against log com/view

Regression equation: Predicted Active engagement = -0.0076 - 0.0659 * log com/view
Slope test: slope = -0.0659, t(123) = -0.535, p = 0.5939; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.20 Direct addressing against log com/view

Regression equation: Predicted Direct addressing = 1.9190 + 0.0414 * log com/view
Slope test: slope = 0.0414, t(123) = 0.262, p = 0.7936; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.21 Use of examples against log com/view

Regression equation: Predicted Use of examples = 1.6728 - 0.0926 * log com/view
Slope test: slope = -0.0926, t(123) = -0.699, p = 0.4861; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.22 Design of visualizations against log com/view

Regression equation: Predicted Design of visualizations = 1.5171 - 0.1243 * log com/view
Slope test: slope = -0.1243, t(123) = -1.029, p = 0.3054; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.23 Matching visualizations-text against log com/view

Regression equation: Predicted Matching visualizations-text = 1.7584 - 0.1986 * log com/view
Slope test: slope = -0.1986, t(123) = -1.918, p = 0.0575; the slope is not statistically significant at alpha = 0.050.

Download this PNG

5.24 Language is comprehensive against log com/view

Regression equation: Predicted Language is comprehensive = 1.6861 - 0.3206 * log com/view
Slope test: slope = -0.3206, t(123) = -4.036, p = <0.001; the slope is statistically significant at alpha = 0.050.

Download this PNG

5.25 Language is precise against log com/view

Regression equation: Predicted Language is precise = 1.5674 - 0.2825 * log com/view
Slope test: slope = -0.2825, t(123) = -2.325, p = 0.0217; the slope is statistically significant at alpha = 0.050.

Download this PNG

5.26 Coherent overall structure against log com/view

Regression equation: Predicted Coherent overall structure = 1.9384 - 0.0834 * log com/view
Slope test: slope = -0.0834, t(123) = -0.875, p = 0.3833; the slope is not statistically significant at alpha = 0.050.

Download this PNG

6 Interpretation guide