Question Type 3: Forecasting another value given a linear fit Bootcamps

The linear model for a bacteria culture growth over time $t$ (hours) is $N(t)=100+25\text{,}$ based on observations from $t=0$ to $t=12$. Estimate $N(20)$ and comment on the prediction’s reliability.

The linear regression model for the relationship between hours studied $x$ and exam score $\bigl(y\bigr)$ is given by $\text{Score} = \bigl(40\bigr) + \bigl(4.5\bigr)x\text{,}$ based on data for $x$ in the range 2 to 8. Forecast the score for a student who studies 10 hours and comment on the reliability of this prediction.

In a calibration experiment, the linear fit between temperature $x$ (°C) and resistance $y$ (Ω) is $R=200+1.5x \text{,}$ valid for 0–100 °C. Find $R$ at 150 °C.

A study of car speed $x$ (km/h) versus fuel consumption $y$ (L/100 km) yields the linear fit $ext{Consumption}=5.2+0.03x ext{,}$for speeds between 40 and 120 km/h. Predict the consumption at 140 km/h and discuss the reliability of this forecast.