10.Find the least squares regression equation for predicting per capita income using the percentage of high school graduates.

Questions 10 through 15 refer to the following:

The following data concerning income and educational attainment for several counties in Alabama were taken from the U.S. Census Website.

County	% High School Grads	Per Capita Income
Autauga	87.6	26168
Chilton	80.1	22045
Coosa	72.9	18080
Dallas	79.0	17611
Elmore	86.8	24711
Jefferson	89.0	28162
Lee	88.7	24951
Lowndes	74.8	18434
Macon	80.5	18385
Montgomery	85.5	26255
Pike	80.0	20180
Shelby	91.6	34117
Sum	996.5	279,099
Sum of Squares	83,144.21	6,772,411,831
∑xy	23,475,084.2

		y = 419082.121 - 57.439x
		y = -39729.72 + 758.510x
		y = -6652.046 + 317.053x
		y = -18096.537 + 474.365x
		y = 22417.029 + 127.884x

QUESTION 11

Find the sample correlation coefficient between per capita income and percentage of high school graduates.

QUESTION 12

Find the value of the t statistic for testing H₀: β₁ = 0 vs. H_A: β₁ ≠ 0.

QUESTION 13

What's the p-value for the test statistic in #12?

QUESTION 14

Do the data provide significant evidence at the .05 level of a linear relationship between per capita income and the percentage of high school graduates?

yes

no

12

robot

QUESTION 15

What is the expected change in per capita income associated with a 1% increase in the proportion of high school graduates?

Solutions

Expert Solution

orchestra answered 2 years ago

Next > < Previous

Related Solutions

The linear regression equation for predicting poverty (%) from the high school graduation rate (%) is...

The linear regression equation for predicting poverty (%) from the high school graduation rate (%) is as follows: ˆ y = 29 -0.2*x High school graduation rate for North Carolina is 22% and the poverty rate is 29.5%. Find the residual for this observation (round your answer to one decimal place)

Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for...

Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(0, 10.8), (3, 11.3), (5, 11.2), (−4, 10.7), (1, 9.3)}

Find an equation for the least-squares regression line for the following data. Round answers to 3...

Find an equation for the least-squares regression line for the following data. Round answers to 3 decimal places (i.e. y = 1.234x -0.123) Advertising Expenses in 1000's of $ (x): 2.4, 1.6, 2, 2.6, 1.4, 1.6, 2, 2.2 Company Sales in 1000's of $ (y ):225, 184, 220, 240, 180, 184, 186, 215 y= ? x+ ? What would the company sales be if $2500 is spent on advertising?

A least-squares simple linear regression model was fit predicting duration (in minutes) of a dive from...

A least-squares simple linear regression model was fit predicting duration (in minutes) of a dive from depth of the dive (in meters) from a sample of 45 penguins' diving depths and times. Calculate the F-statistic for the regression by filling in the ANOVA table. SS df MS F-statistic Regression Residual 1628.4056 Total 367385.9237

For the dataset describing year, US Return, and Overseas Return 1. Find the least-squares regression equation...

For the dataset describing year, US Return, and Overseas Return 1. Find the least-squares regression equation of overseas returns on U.S. returns. 2. In 1997, the return on U.S. stocks was 33.4%. Use the regression line to predict the return on overseas stocks. (You may either calculate this by hand or use SAS output.) The actual overseas return was 2.1%. Are you confident that predictions using the regression line will be quite accurate? Why? DATA 1971 29.6 14.6 1972 36.3...

CHAPTER 7: REGRESSION/PREDICITION Key Terms ---------------------------------------------------------------------------------------------------------------------------- Least squares prediction equation --- The equation that minimizes the...

CHAPTER 7: REGRESSION/PREDICITION Key Terms ---------------------------------------------------------------------------------------------------------------------------- Least squares prediction equation --- The equation that minimizes the total of all squared prediction errors for known Y scores in the original correlation analysis. Standard error of prediction --- A rough measure of the average amount of predictive error Squared correlation coefficient --- The proportion of the total variance in one variable that is predictable from its relationship with the other variable Variance interpretation of r²---The proportion of variance explained by, or predictable...

Suppose there is a linear association between crime rate and percentage of high school graduates. a)...

Suppose there is a linear association between crime rate and percentage of high school graduates. a) State the full and reduced model b)Obtain SSE(F), SSE(R), df(F), fd(R), test statistics F for the general linear test and decision rule. crime rate, high school grad % 8487 74 8179 82 8362 81 8220 81 6246 87 9100 66 6561 68 5873 81 7993 74 7932 82 6491 75 6816 82 9639 78 4595 84 5037 82 4427 79 6226 78 10768 73...

Q1. Write down the equation of the regression straight line (the least-squares line)

Q1. Write down the equation of the regression straight line (the least-squares line) Q2. For an increase of 1 mg of fertiliser applied, what is the average change in the wet weight of maize plants? Q3. How are the two variables associated with each other? (Answer in 1 or 2 sentences)Q4. Determine the average weight of plants grown with 100mg of fertiliser applied. (round up your answer to 2 decimal places)Q5. Determine the average weight of plants grown with...

What is the least squares method and how is it used to find the estimated regression...

What is the least squares method and how is it used to find the estimated regression equation? What is the role of least squares method in calculating coefficient of determination? Explain

What is the least squares method and how is it used to find the estimated regression...

What is the least squares method and how is it used to find the estimated regression equation? What is the role of least squares method in calculating coefficient of determination? Explain.

Subjects

		yes
		no
		12
		robot