For Han

3d Plot

data <- read.csv("data_temp.csv")
summary(data)

##     LC_mean      Autonomy_mean    Meaning_mean      LCxAuto      
##  Min.   :1.143   Min.   :1.000   Min.   :1.000   Min.   : 1.143  
##  1st Qu.:3.857   1st Qu.:4.000   1st Qu.:4.000   1st Qu.:16.095  
##  Median :4.571   Median :5.000   Median :4.833   Median :21.429  
##  Mean   :4.425   Mean   :4.651   Mean   :4.581   Mean   :21.068  
##  3rd Qu.:5.000   3rd Qu.:5.333   3rd Qu.:5.167   3rd Qu.:25.714  
##  Max.   :6.000   Max.   :6.000   Max.   :6.000   Max.   :36.000

#meaning = LC X1 + Autonomy X2 + LX*Auto + e
m1 <- lm(Meaning_mean ~ LC_mean + Autonomy_mean + LC_mean * Autonomy_mean, 
         data = data)
m1

## 
## Call:
## lm(formula = Meaning_mean ~ LC_mean + Autonomy_mean + LC_mean * 
##     Autonomy_mean, data = data)
## 
## Coefficients:
##           (Intercept)                LC_mean          Autonomy_mean  
##              -0.32942                0.80634                0.63860  
## LC_mean:Autonomy_mean  
##              -0.07726

summary(m1)

## 
## Call:
## lm(formula = Meaning_mean ~ LC_mean + Autonomy_mean + LC_mean * 
##     Autonomy_mean, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3631 -0.4434  0.0961  0.5577  2.3189 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           -0.32942    0.60689  -0.543   0.5875    
## LC_mean                0.80634    0.15570   5.179 3.38e-07 ***
## Autonomy_mean          0.63860    0.13931   4.584 5.92e-06 ***
## LC_mean:Autonomy_mean -0.07726    0.03286  -2.351   0.0192 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.773 on 449 degrees of freedom
## Multiple R-squared:  0.4147, Adjusted R-squared:  0.4108 
## F-statistic: 106.1 on 3 and 449 DF,  p-value: < 2.2e-16

require(plotly)

## Loading required package: plotly

## Loading required package: ggplot2

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

require(magrittr)

## Loading required package: magrittr

plot_ly(data = data) %>%
  add_trace(x = ~LC_mean, 
            y = ~Autonomy_mean, 
            z = ~Meaning_mean, 
            mode = "markers", 
            type = "scatter3d",
            marker = list(size = 5, color = "blue", symbol = 104), 
            name = "Observations") %>% 
  add_trace(z = m1$fitted.values, 
            x = ~LC_mean, 
            y = ~Autonomy_mean, 
            type = "mesh3d", 
            name = "Fitted values") %>%
  layout(scene = list(xaxis = list(title = 'LC_mean'),
                      yaxis = list(title = 'Autonomy_mean'),
                      camera = list(eye = list(x = -0.5, y = 2, z = 0)),
                      zaxis = list(title = 'Meaning_mean'), 
                      aspectmode='cube'))