Results

Linear Regression

Model Summary - cog_fun
Model	R	R²	Adjusted R²	RMSE
M₀	0.000	0.000	0.000	9.883
M₁	0.078	0.006	0.005	9.860

Note. M₁ includes tea

ANOVA
Model		Sum of Squares	df	Mean Square	F	p
M₁	Regression	421.093	1	421.093	4.331	0.038
	Residual	69412.968	714	97.217
	Total	69834.061	715

Note. M₁ includes tea
Note. The intercept model is omitted, as no meaningful information can be shown.

Coefficients
Model		Unstandardized	Standard Error	Standardized	t	p
M₀	(Intercept)	50.612	0.369		137.034	< .001
M₁	(Intercept)	49.218	0.764		64.382	< .001
	tea	0.460	0.221	0.078	2.081	0.038

Looking at the Coefficients output above, we can see that we have a model that significantly improves our ability to predict cognitive functioning. The positive standardized beta value (0.078) indicates a positive relationship between number of cups of tea drunk per day and level of cognitive functioning, in that the more tea drunk, the higher your level of cognitive functioning.

We can then use the model to predict level of cognitive functioning after drinking 10 cups of tea per day. The first stage is to define the model by replacing the b-values in the equation below with the values from the Coefficients output. In addition, we can replace the X and Y with the variable names so that the model becomes:

Cognitive Functioning_i = b₀ + b₁Tea drinking_i

= 49.218 + (0.460 x Tea drinking_i)

We can predict cognitive functioning, by replacing Tea drinking in the equation with the value 10:

Cognitive Functioning_i = 49.218 + (0.460 x 10) = 53.818

Therefore, if you drank 10 cups of tea per day, your predicted level of cognitive functioning would be 53.818.