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

Given the regression equation $y = 2.5x - 1.3$ fitted to data with $x$ in the range $[1,5]$, forecast $y$ when $x = 10$ and comment on the reliability of this prediction.

Hours studied and exam score: $(2,65)$, $(4,75)$, $(6,83)$, $(8,90)$, $(10,95)$. Find the regression line, forecast the score at 9 hours, and comment on the reliability.

Pressure (atm) and temperature (K): $(1,200)$, $(2,250)$, $(3,300)$, $(4,350)$, $(5,400)$. Find the regression line, forecast temperature at $6$ atm, and comment on reliability.

Given the following bivariate data: $(1,2)$, $(2,3)$, $(3,5)$, $(4,4)$, $(5,6)$. Find the least-squares regression line of $y$ on $x$, forecast $y$ when $x=6$, and comment briefly on the reliability of this prediction.

Given three data points $(10,5)$, $(15,9)$, $(20,14)$, find the least-squares regression line of $y$ on $x$, forecast $y$ when $x=25$, and comment on the reliability of the forecast.

Advertising budget (\k) and sales revenue (\k): $(2,30)$, $(4,45)$, $(6,55)$, $(8,70)$, $(10,85)$, $(12,95)$. Determine the regression line, forecast revenue at $15$k, and comment on reliability.

Age (years) and systolic blood pressure (mmHg): $(30,120)$, $(40,130)$, $(50,140)$, $(60,150)$, $(70,160)$, $(80,170)$. Find the regression line, forecast blood pressure at age $85$, and comment on reliability.

Time (hours) and units produced: $(1,15)$, $(2,22)$, $(3,28)$, $(4,34)$, $(5,38)$, $(6,45)$. Determine the regression line of units produced ($y$) on time ($x$), predict production at $x=8$ hours, and comment on reliability.

Temperature (°C) and ice-cream sales (units): $(20,200)$, $(22,215)$, $(24,230)$, $(26,250)$, $(28,270)$, $(30,290)$, $(32,310)$. Find the regression line, forecast sales at $35$°C, and comment on reliability.

Years of experience and salary $(k):$(1,30)$,$(3,38)$,$(5,46)$,$(7,55)$,$(9,63)$,$(11,70)$,$(13,78)$,$(15,85)$. Determine the regression line, forecast salary at 12 years, and comment on reliability.

Distance (miles) and fuel consumption (gallons): $(50,2.8)$, $(100,5.6)$, $(150,8.3)$, $(200,11.1)$, $(250,13.9)$, $(300,16.7)$, $(350,19.4)$, $(400,22.2)$. Find the regression line, forecast consumption at $450$ miles, and comment on reliability.