1. Homework: pg. 266 #3
A. The relationship is strong, negative, and slightly curved. B. Yes. The scatterplot for the transformed data shows a clear linear relationship.

2. C. R-sq=0. 9958, indicates almost a perfect fit
C. R-sq=0.9958, indicates almost a perfect fit. The residual plot does show a pattern, which should cause some concern, however, our equation is a pretty good fit. D. This and the residual plot indicate that this linear model is an excellent fit for the data. E. The first model predicts: ; the second model predicts: The predictions are very close.

3. 4.1 Exponential Growth

4. Linear vs. Exponential Growth
linear growth—when fixed increment is added to the variable in each equal time period—increases by a fixed amount in each equal time period
𝑦=𝑎+𝑏𝑥
exponential growth—when a variable is multiplied by a fixed number in each equal time period—increases by a fixed percent of the previous total in each equal time period
𝑦=𝑎∙ 𝑏 𝑥

5. Algebra you need to know:

6. Bacteria Example
a) Make a scatterplot of the data. Describe the form of the relationship
Hours
# of Bacteria
1.0
1.8
1.5
2.4
2.0
3.1
2.5
4.3
3.0
5.8
3.5
8.0
4.0
10.6
4.5 14 5 18
b) Take the natural log of the y-values. What equation of the LSRL?
c) Create new scatterplot, residual plot, and find r2 value.

7. Transforming Equations

8. Planet Example
a) Make a scatterplot of the data. Describe the form of the relationship
Planet
Distance
Mercury 36
Venus 37
Earth 93
Mars
142
Jupiter
484
Saturn
887
Uranus
1765
Neptune
2791
Pluto
3654
b) Take the log of the y-values. What equation of the LSRL?
c) Create new scatterplot, residual plot, and find r2 value.

9. Transforming Equations

10. Review
Steps: 1. Make scatterplot of original # in data set 2. If exponential—take log or ln of y-values (does not matter which one) 3. Recreate scatterplot, get equation of line, make residual plot, and find r2 Scatterplot should make a line; residual plot should be scattered 4. Transform equation into y= form

11. HW: pg 276 #5-6