The protein content for the 15 bean varieties has a mean of 12.2 grams and a standard deviation of 5.3 grams. The mean carbohydrate content is 33.6 grams with a standard deviation of 15.7 grams. The correlation is 0.84 . Which of the following expressions represents the slope of the leastsquares regression of \( y= \) protein content on \( x= \) carbohydrate content? \( \frac{(0.84)(5.3)}{(15.7)} \) \( \frac{(0.84)(122)}{(33.6)} \) \( \frac{(0.84)(15.7)}{(5.3)} \) \( \frac{(0.84)(33.6)}{(12.2)} \) \( \frac{(33.6)}{(0.84)(12.2)} \)
Added by Logan C.
Close
Step 1
The slope (b) of the regression line predicting y from x is given by the formula: \[ b = \frac{r \cdot s_y}{s_x} \] where \( r \) is the correlation coefficient between x and y, \( s_y \) is the standard deviation of y, and \( s_x \) is the standard deviation of Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 71 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The computer output shown below gives the least-squares regression line for calories and protein (in grams) in one cup of 11 varieties of dried beans. Describe the slope in context:
Adi S.
2. ANOVA method for significance test about slope: The table below is ANOVA table in R: Analysis of Variance Table Response: concentration Df Sum Sq Mean Sq F value Pr(>F) area 1 1130.15 1130.15 xxxx 2.863e-13 *** Residuals 18 57.72 xxxxx --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 * Hypotheses: * Test statistic: * p-value 3. What is the coefficient of determination for this regression line? Interpret it.
The data shows sugar consumption (pounds per year per person) in the United States for a sample of 5 years: Year Sugar Consumption 1900 46 1920 71 1940 77 1960 79 1980 86 2000 106 The mean of year is 1950 and the standard deviation of year is 37.4. The mean of sugar consumption is 77.5 and the standard deviation is 19.6. The correlation coefficient between Year and Sugar consumption is 0.95. [Useful formulas: slope = rSy/Sx and intercept = mean of Y - (slope * mean of X)] According to the regression, what will sugar consumption be in 2020? Round your answer to the nearest integer. Do not use decimal places in your answer.
David N.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD