residuals, exponential and powers

Question 1

linear

Answer 1

y = a + bx (constant increase)

Question 2

power

Answer 2

y = ax^b

Question 3

exponential

Answer 3

y = ae^bx (constant % increase or increase by a constant factor. Constant increase in ln(y)

Question 4

residuals and residual plots

Answer 4

analysis of pattern of residuals will allow us to decide which model is most suitable - U-shaped or upside down U are not the best model

Question 5

residuals plot by hand

Answer 5

use a hat and b hat equations

Question 6

residual plot excel

Answer 6

regression, residuals

Question 7

predicted t

Answer 7

the best fitted value correspond to the values predicted by the best fit for t

Question 8

residuals

Answer 8

the difference between those t predictions and the actual values of t that were observed

• can be shown on graphs as lines sticking out the side
• can use a residual plot - if there is a pattern then a straight line might not be the best fit

Question 9

recognising curved relationships

Answer 9

• U shaped might be exponential (on a regression plot)

- upside down U might be logs

Question 10

exponential to log

Answer 10

if y = ae^bx, ln(y) = ln(a) + bx (linear function)

• find line of best fit in ln(y) and x values
• b is slope of the regression line, a is given by e^cinstant

Question 11

power to log

Answer 11

if y = ax^b then ln(y) = ln(a) + bln(x) (linear function)

find the line of best fit with ln(y) and ln(x) values

Question 12

residuals goal

Answer 12

plot exponential and logs to see which fits better

Question 13

fitting a linear, power or exponential trendline in excel

Answer 13

• use residual plots to determine which of linear, power or exponential is best
• use the chart wizard to produce a plot. when adding trendline, tick linear, power or exponential as appropriate, a power model requires the 2 variables are zero together