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How should I interpret the following results? My thesis takes a long at the underlying values of political preference and the consumption quantities of meat-replacements products (such as vegetarian burgers) to see if any assumptions can be made about the relationship between these two variables. Thoughts on income inequality is defined as a socio-economic left-right meausure, while a 'liberal-conservative' measure is measured by 'thought on euthanasia, european unification and immigrant culture' and 'thoughts on family values'. The rest are control variables. I don't exactly know how to explain the significance levels for each variable in terms of their relationship with meat-replacement quantities.

I hope anyone is able to help.

  • $\begingroup$ What analysis did you perform (linear regression? Logistic regression? Something else?) How is your dependent variable coded (e.g. yes/no or something else)? $\endgroup$ – Peter Flom - Reinstate Monica Nov 26 '19 at 14:06

If I understood you correctly, your response variable $y$ measures consumption quantities of meat-replacements products, and you are trying to study the relation between this variable and political preferences measured as "Thoughts on income inequality", "Thoughts on family" etc. You have performed a multiple linear regression model, and obtained the following equation: $$\hat y_i = \hat\beta_0 + \hat\beta_1x_{i1} + \ldots + \hat\beta_px_{ip}$$

The first column in the table gives you the estimates for the parameters of the model. This means, applied to your data, that you will predict the consumption quantities of meat-replacements products as

$$\hat y_i = 1.547 - 0.038x_{i1} - 0.075 x_{i2} + \ldots -0.001x_{i8}$$

Loosely speaking, the second column measures a margin error on your estimation of the $\beta$ coefficients that will be used in columns 4 and 5.

The third column offers you the standardized coefficients. The original $\beta$ coefficients from the first column are expressed in the same units as the variables that they refer to. This means, for example, that if $x_1$ is expressed in euros then $\beta_1$ will be expressed in euros. Since each coefficient may be expressed in different units, this makes it difficult to compare the coeefficients and see which ones are affecting more. The standardized coefficients are the coefficients obtained when you get rid of the units. So you can compare the absolute value of the standardized coefficients, the higher the absolute value of the $\beta$ coefficient, the stronger the effect. In this particular case, the standardized coefficient for $\beta_1=-0.025$ while the standardized coefficient for $\beta_2=-0.047$ so we can conclude that "Thoughts on eutanasia european unification etc" has a stronger effect than "Thoughts on income inequality" (because 0.047 > 0.025)

Finally, the 4º and 5º columns refer to a hypothesis test for the coefficients. For each coefficient, you perform the test:

$$H_0: \beta_j=0$$ $$H_1: \beta_j\neq0$$

For doing this test, you calculate the so-called test statistic for eachg coefficient as $$t=\frac{\hat\beta_j}{SE(\hat\beta_j)}$$ For example, in the case of $\beta_1$, the 4º column displays the value of the test statistic calculated as be $-0.038/0.045=-0.829$

The last column offers you the p-value for this test. Given a significance level (The usual value for the significance level is 0.05 or 0.1) you compare the p-value with this level. If the p-value is smaller than the significance level this means that you reject the null hypothesis $H_0$ therefore supporting the alternative hypothesis $H_1$. The alternative hypothesis was $H_1: \beta_j\neq0$ so by supporting this you are saying that the variable associated to this $\beta_j$ is statistically significant for your model.

For example, the p-value associated to $\beta_1=0.4>0.05$ so for a significance level of 5%, we fail to reject the null hypothesis. This variable is not statistically significant in your model (it does not help explaining the behaviour of consumption quantities of meat-replacements products). The p-value of $\beta_4=0<0.05$ meaning that thought on family values is statistically significant and affects quite much the behaviour of consumption quantities of meat-replacements products.

Now, regarding the variables that appear as not statistically significant, this may be due to 2 possible reasons:

The variables that appear as "not significant" may display this behaviour for one of two reasons:

  1. The variable is not statistically significant because it is not linearly related to your response variable consumption quantities of meat-replacements so it is not providing any useful information related to the response variable. This means that knowing this variable does not help at all on predicting your response variable.

    2) The variable is actually related to your response variable, but is also related to yet another variable that is already included in your model and that is being displayed as significant. For example, imagine for a second that "Thoughts on income inequality" was related to "highest level of education". Being related would mean that some of the information that "Thoughts on income inequality" would provide, would be already being provided by "highest level of education". So "Thoughts on income inequality" is no longer useful in the model and appears as not significant.

In order to detect which is the case for your not significant variables, the usual procedure is to perform univariate regression models. This means, to define a model that tries to explain consumption quantities of meat-replacements products as a function of just one of your variables at a time. If any of the variables is individually significant but non-significant in the multivariate model, is because of the case (2). If the variable is individually and in the multivariate model not significant, then you are in case (1).

  • $\begingroup$ Thank you, this helps immensely. Thank you for taking the time to answer this question. Going from your explanation, I only have three variables which significantly explain the consumer behaviour with respect to meat-replacements, right? What do I say about the variables which are considered 'not significant' in explaining this relationship in a discussion? $\endgroup$ – Eltini1949 Nov 26 '19 at 12:21
  • $\begingroup$ I have make an edit on the answer, check it out. $\endgroup$ – Álvaro Méndez Civieta Nov 26 '19 at 14:45

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