Consider the following set of data.
The equation of the least squares line fitted to this data is approximately $y=3.15-0.18x$y=3.15−0.18x.
$x$x | $0.8$0.8 | $1.77$1.77 | $2.7$2.7 | $3.62$3.62 | $4.9$4.9 | $5.7$5.7 | $7$7 | $8.6$8.6 | $10.1$10.1 |
---|---|---|---|---|---|---|---|---|---|
$y$y | $3.4$3.4 | $2.9$2.9 | $2.5$2.5 | $2.4$2.4 | $1.9$1.9 | $1.9$1.9 | $1.8$1.8 | $1.7$1.7 | $1.54$1.54 |
Predict the value of $y$y when $x=3$x=3 using the least square line.
Is this an interpolation or extrapolation?
Interpolation
Extrapolation
Consider the following set of data.
The equation of the least squares line fitted to this data is approximately $y=3.15-0.18x$y=3.15−0.18x.
Consider the following set of data.
The equation of the least squares line fitted to this data is approximately given by $\text{Average test score}=70.34-1.92\times\text{Number of tests}$Average test score=70.34−1.92×Number of tests.
A least squares regression line is given by $y=3.59x+6.72$y=3.59x+6.72.
Create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate.
Describe the value of mathematical modelling and how it is used in real life to inform decisions.