Load the `carsmall`

data set.

The variable `Model_Year`

contains data for the year a car was manufactured, and the variable `Cylinders`

contains data for the number of engine cylinders in the car. The `Acceleration`

and `Displacement`

variables contain data for car acceleration and displacement.

Use the `table`

function to create a table of factor values from the data in `Model_Year`

and `Cylinders`

.

Create a matrix of response variables from `Acceleration`

and `Displacement`

.

Perform a two-way MANOVA using the factor values in `tbl`

and the response variables in `y`

.

maov =
2-way manova
Y1,Y2 ~ 1 + Year + Cylinders
Source DF TestStatistic Value F DFNumerator DFDenominator pValue
_________ __ _____________ ________ ______ ___________ _____________ __________
Year 2 pillai 0.084893 2.1056 4 190 0.081708
Cylinders 2 pillai 0.94174 42.27 4 190 2.5049e-25
Error 95
Total 99
Properties, Methods

`maov`

is a two-way `manova`

object that contains the results of the two-way MANOVA. The output displays the formula for the MANOVA model and a MANOVA table. In the formula, the car acceleration and displacement are represented by the variables `Y1`

and `Y2`

, respectively. The MANOVA table contains a small *p*-value corresponding to the `Cylinders`

term in the MANOVA model. The small *p*-value indicates that, at the 95% confidence level, enough evidence exists to conclude that `Cylinders`

has a statistically significant effect on the mean response vector. `Year`

has a *p*-value larger than 0.05, which indicates that not enough evidence exists to conclude that `Year`

has a statistically significant effect on the mean response vector at the 95% confidence level.

Use the `barttest`

function to determine the dimension of the space spanned by the mean response vectors corresponding to the factor `Year`

.

The output shows that the mean response vectors corresponding to `Year`

span a point, indicating that they are not statistically different from each other. This result is consistent with the large *p*-value for `Year`

.