What's WRONG with my multiple regression model

Question

I am working on a regression model, more precisely, multiple regression model for predicting one single value. I have a dataset of cars and some technical data.

For example, I have the following prediction for the following car data:

Make: Volvo 
Model: XC90 T8 Recharge AWD 
Doors: 4 
Seats: 7 
SeatsMin: 7 
SeatsMax: 7 
Dimensions: 4950x1931x1776 
Length: 4950 
Width: 1931 
Height: 1776 
WheelBase: 2984 
Weight: 2320 
MaxWeight: 2980 
TrunkVolMin: 262 
TrunkVolMax: 1816 
TankVolume: 70 
Electric: Electric or hybrid 
TurboCharged: 1: Turbo charged engine 
Kompressor: 1: Kompressor charged engine 
Displacement: 1969 
EnginePower: 288(390)/6000 
EngineTorque: 640/2200 
MaxPower: 288.00 
MaxTorque: 640.00 
Druve: All wheel drive 
FrontWheelDrive: Front wheel drive 
RearWheelDrive: Rear wheel drive 
Gears: 8 
Automatic: Automatic gearbox 
Acceleration: 5.8 
MaxSpeed: 180 
FuelConsumption: 2.1 S 
CO2: 57 
FuelType: S 
Predicted_Acceleration: 5.66731 
Residuals: .13269

Acceleration by default is 5.8, the model gives 5.66731, meaning it is off by 0.1 or something. According to the model summary, $R^2$ is roughly 75.9% percent accurate.

EDIT: I do not know for sure, what other bits of data here can be used to form a more accurate model. I haven't made any dummy variables yet. Not decoded into binary.

Answer 1

Your comment "Now, I am not good with cars, so I do not know exactly what parts of the data here can help achieve better output" is very insightful! You've correctly identified your problem, and the solution is not in the data or the model. The solution is finding out more about how cars accelerate.

I would advise you to find someone who does know a lot about cars, and ask them a lot of questions. You might learn things like:

• "Turbo charged engines always accelerate faster/slower than Kompressor charged engines"
• "If you want a car that accelerates fast, you would look for XXX and YYY but avoid ZZZ" (You would then know to include those things in your model)
• "XXX increases acceleration up to a point but then levels off" (Maybe you would then include XXX in your model as a polynomial term instead of a linear term)
• "For a front wheel drive car XXX is important but for a rear-wheel drive car XXX makes no difference" (Then you might include an interaction term in your model)
• "Error of 0.8 is really close, that's very good accuracy" or "Error of 0.8 is really big, that's terrible accuracy" (Then you would know how useful your model actually is)

I also do not know anything about cars, so I can't answer these questions. They may not even be the right questions! But for a real-world modelling task, understanding the real-world meaning of the data is never time wasted.

Answer 2

It is not clear what your question is, especially as the prediction looks amazingly accurate to me: 5.67 versus 5.8 is just an error of about 2%. Maybe you are misinterpreting the reported value of $R^2$ as a measure for accuracy, which it is not.

A nice thing about linear models is that they also estimate the accuracy of the prediction by means of a "prediction interval"*). It estimates, under the assumption that the model is correct, an interval in which the response value will be observed 95% of the times for the given predictor values. In R, e.g., you can obtain it with

predict(model, data.frame(x1=val1, x2=val2, 
          ...), interval="predict")

This way, you can estimate the accuracy of the prediction even when the true value is unknown.

*) Edit: in the original version of the answer, I called the "prediction interval" a "confidence interval", but as pointed out by @whuber, this term is reserved for parameter estimates.