Bring project data to class tomorrow.

Section 3.2 Day 2

Activity 3.2a, Page 117

Activity 3.2a, Page 117 # 6) Does the plot look linear? Should it?

Activity 3.2a, Page 117 # 6) Does the plot look linear? Should it? The plot should look linear as an increase of one sheet of paper adds a fixed amount to the total thickness.

# 8 Thickness = y-intercept + (slope)sheets Thickness = 3.0 + (0.0668)sheets What does y-intercept tell us? What does slope tell us? What is the estimate of the thickness of one sheet of paper?

# 8 Thickness = y-intercept + (slope)sheets Thickness = 3.0 + (0.0668)sheets What does y-intercept tell us? Thickness of cover as this is the thickness if no sheets are included. What does slope tell us? What is the estimate of the thickness of one sheet of paper?

# 8 Thickness = y-intercept + (slope)sheets Thickness = 3.0 + (0.0668)sheets What does slope tell us? The estimate of the thickness of one sheet of paper What is the estimate of the thickness of one sheet of paper?

# 8 Thickness = y-intercept + (slope)sheets Thickness = 3.0 + (0.0668)sheets What does slope tell us? The estimate of the thickness of one sheet of paper What is the estimate of the thickness of one sheet of paper? 0.0668 mm

# 9: Precision of Estimate Use the information in your graph to discuss the precision of your estimate in step 8 (estimate of the thickness of one sheet of paper).

# 9: Precision of Estimate Use the information in your graph to discuss the precision of your estimate in step 8. We should recognize there are two likely sources of error:

# 9: Precision of Estimate Use the information in your graph to discuss the precision of your estimate in step 8. We should recognize there are two likely sources of error: (1) measurement error and

# 9: Precision of Estimate Use the information in your graph to discuss the precision of your estimate in step 8. We should recognize there are two likely sources of error: (1) measurement error and (2) error in fitting a line through the points (based on your judgment)

# 9: Precision of Estimate We expect some inaccuracy in each measurement since we are measuring to the nearest millimeter; some will be too small and some will be too large. By using the line of best fit to estimate the slope, we are averaging out those errors.

# 10 How would your line have changed if you had not included the front cover? Thickness = 3.0 + (0.0668)sheets

# 10 How would your line have changed if you had not included the front cover? Thickness = (0.0668)sheets The y-intercept should be very close to 0. Why?

# 10 How would your line have changed if you had not included the front cover? Thickness = (0.0668)sheets The y-intercept should be very close to 0. If there are 0 pages, the total thickness would be 0.

Page 118, D3 Write down your answers to these questions.

Page 118, D3 a) Gas costs $2.60 per gallon; y = 2.60x y represents: x represents:

Page 118, D3 a) Gas costs $2.60 per gallon; y = 2.60x y represents the cost of the purchase x represents number of gallons purchased

Page 118, D3 b) Car averages 30 mi/gal; y = 30x y represents: x represents:

Page 118, D3 b) Car averages 30 mi/gal; y = 30x y represents miles driven x represents number of gallons used

Page 118, D3 c) “A pint’s a pound the world around.” y = x y represents: x represents:

Page 118, D3 c) “A pint’s a pound the world around.” y = x y represents weight in pounds x represents volume of the liquid

Line of Best Fit Line through points with about one-half of the points above and about one-half of the points below.

Why Fit a Line to Set of Data? Two main reasons to do so.

Two main reasons to fit a line to a set of data: 1) to find a summary or model that describes relationship between two variables

Two main reasons to fit a line to a set of data: 1) to find a summary or model that describes relationship between two variables 2) to use the line to predict value of y when you know value of x

To make a reasonable prediction using the line, what needs to be true about: A) shape of data? B) strength of relationship?

To make a reasonable prediction, what needs to be true about: A) shape of data? linear B) strength of relationship?

To make a reasonable prediction, what needs to be true about: A) shape of data? linear B) strength of relationship? Stronger the better

Variables In previous math classes: x was called the independent variable. y was called the dependent variable.

Variables Now, the variable on the x-axis is called the __________ or __________ variable. The variable on the y-axis is called the __________ or __________ variable.

Now, the variable on the x-axis is called the predictor or explanatory variable. The variable on the y-axis is called the __________ or __________ variable.

The variable on the x-axis is called the predictor or explanatory variable. The variable on the y-axis is called the predicted or response variable.

Find the slope of the line that passes through the points (1960, 0 Find the slope of the line that passes through the points (1960, 0.80) and (2000, 4.80)

Find the slope of the line that passes through the points (1960, 0 Find the slope of the line that passes through the points (1960, 0.80) and (2000, 4.80) Slope =

Find the slope of the line that passes through the points (1960, 0 Find the slope of the line that passes through the points (1960, 0.80) and (2000, 4.80) m = 0.10

Find the equation for that line in slope- intercept form, y = mx + b through the points (1960, 0.80) and (2000, 4.80)

Find the equation for that line in slope- intercept form, y = mx + b If we use (1960, 0.80): 0.80 = (0.10)(1960) + b b = -195.20

Find the equation for that line in slope- intercept form, y = mx + b If we use (1960, 0.80): 0.80 = (0.10)(1960) + b b = -195.20 Equation is y = 0.10x – 195.20

Equation is y = 0.10x – 195.20 Recall, in statistics, the equation is written with y-intercept first. So, y = -195.20 + 0.10x

Page 133, E10

Page 133, E10 (a) Fewest calories: Little Caesar’s Original Round and Pizza Hut’s Hand Tossed

Page 133, E10 (a) Least fat: Little Caesar’s Original Round and Pizza Hut’s Hand Tossed

Page 133, E10 (a) Region of graph with pizzas with most fat: right side of graph

Page 133, E10 (b) I – E II – D III – A IV – C V – B

Page 133, E10 (c) i. A; predicted calories too high because line is above all the points

Page 133, E10 (c) ii. E; predicted calories too low because line is below most of the points

Page 133, E10 (c) Overestimate calorie count for lower-fat and underestimate for higher-fat pizza iii. B

Page 133, E10 (c) Underestimate for lower-fat and overestimate for higher-fat pizza iv. D

Page 133, E10 (c) v. C fits data best overall (line of best fit)

Questions?