Question

> muncy = lm(hit_distance~launch_speed, data=muncy)

> summary(muncy)

Call:

lm(formula = hit_distance ~ launch_speed, data = muncy)

Residuals:

Min 1Q Median 3Q Max

-258.24 -105.23 23.29 116.06 174.73

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -240.8429 36.6769 -6.567 1.46e-10 ***

launch_speed 4.8800 0.4022 12.134 < 2e-16 ***

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 122.4 on 438 degrees of freedom

Multiple R-squared: 0.2516, Adjusted R-squared: 0.2499

F-statistic: 147.2 on 1 and 438 DF, p-value: < 2.2e-16

a) Use R to find the equation of the regression line relating Y=hit distance and x=launch speed. Write the equation of the regression line.

b) Refer to the output in part a to explain why there is definitely a correlation between these quantities, but no one would ever attempt to predict hit distance from the launch speed variable only.

Answer #1

Can you give me a simple interpretation of this output?
Call:
lm(formula = NOCRF ~ Mktrf + HML + SMB + SMB2)
Residuals:
Min
1Q Median
3Q Max
-10.1560 -0.6880 -0.0254 0.6660 21.9700
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.01163 0.02800
-0.415 0.678
Mktrf 1.25614
0.02389 53.540 <2e-16 ***
HML
2.01719 0.04238 47.602 <2e-16 ***
SMB -0.05150
0.04769 -1.080
0.280
SMB2 0.03180
0.03545 0.897 0.372
---
Signif. codes: 0 ‘***’ 0.001...

4.-Interpret the following regression model
Call:
lm(formula = log(Sale.Price) ~ Lot.Size + Square.Feet + Num.Baths +
dis_coast + API.2011 + dis_fwy + dis_down + Pool, data = Training)
Residuals:
Min 1Q Median 3Q Max
-2.17695 -0.23519 -0.00112 0.26471 1.02810
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.630e+00 2.017e-01 47.756 < 2e-16 ***
Lot.Size -2.107e-06 3.161e-07 -6.666 4.78e-11 ***
Square.Feet 2.026e-04 3.021e-05 6.705 3.71e-11 ***
Num.Baths 6.406e-02 2.629e-02 2.437 0.015031 *
dis_coast -1.827e-05 6.881e-06 -2.655 0.008077 **
API.2011 3.459e-03 2.356e-04...

Using the following data taking out of R (summary):
Call:
lm(formula = dys_detect ~ fin_loss, data = Lab5, na.action =
na.exclude)
Residuals:
Min 1Q Median 3Q Max
-582.66 -274.75 13.53 273.92 589.06
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 385.362 77.360 4.981 8.72e-07 ***
fin_loss 3.248 1.523 2.133 0.0334 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 316.6 on 498 degrees of freedom
Multiple R-squared: 0.009052, Adjusted R-squared:...

8.) Now, do a simple linear regression model for LifeExpect2017
vs. AverageDailyPM2.5. For credit, provide the summary
output for this simple linear regression model.
> Model2 <- lm(LifeExpect2017~ AverageDailyPM2.5)
> summary(Model2)
Call:
lm(formula = LifeExpect2017 ~ AverageDailyPM2.5)
Residuals:
Min 1Q Median 3Q Max
-17.1094 -1.7516 0.0592 1.7208 18.4604
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 81.6278 0.2479 329.23 <2e-16 ***
AverageDailyPM2.5 -0.4615 0.0267 -17.29 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘...

Consider the following regression run in R, which uses engine
size in liters, horsepower, weight, and domestic vs foreign
manufacturer to predict mileage:
------------------------------------------------------------------------------------------------------
> summary(lm(highwaympg~displacement+hp+weight+domestic))
Call:
lm(formula = highwaympg ~ displacement + hp + weight +
domestic)
Residuals:
Min 1Q Median 3Q
Max
-6.9530 -1.6997 -0.1708 1.6452 11.4028
Coefficients:
Estimate
Std. Error t value Pr(>|t|)
(Intercept) 53.849794 2.090657 25.757 < 2e-16
***
displacement 1.460873 0.748837
1.951 0.0543 .
hp -0.009802
0.011356 -0.863 0.3904
weight -0.008700
0.001094 -7.951 6.23e-12 ***
domestic -0.939918
0.762175 -1.233 0.2208
---...

3.) Now, you are going to run the multivariable linear
regression model you just created.
For credit: Provide your model command and summary
command below along with all the output for your model
summary.
Model1 <- lm(LifeExpect2017~HouseholdIncome + Diabetic +
FoodInsecure + Uninsured + DrugOverdoseMortalityRate )
> summary(Model1)
Call:
lm(formula = LifeExpect2017 ~ HouseholdIncome + Diabetic + FoodInsecure +
Uninsured + DrugOverdoseMortalityRate)
Residuals:
Min 1Q Median 3Q Max
-5.4550 -0.8559 0.0309 0.8038 7.1801
Coefficients:
Estimate Std. Error t value Pr(>|t|)...

Marketing date on sales is presented for youtube. data are the
advertising budget in thousands of dollars along with the sales.
The experiment has been repeated 200 times with different budgets
and the observed sales have been recorded. The simple linear
regression model was fitted:
##
## Call:
## lm(formula = sales ~ youtube, data = marketing)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.06 -2.35 -0.23 2.48 8.65
##
## Coefficients:
## Estimate Std. Error t...

3.) Now, you are going to run the multivariable linear
regression model you just created.
For credit: Provide your model command and summary
command below along with all the output for your model
summary.
Model1 <- lm(LifeExpect2017~HouseholdIncome + Diabetic + FoodInsecure + Uninsured + DrugOverdoseMortalityRate )
> summary(Model1)
Call:
lm(formula = LifeExpect2017 ~ HouseholdIncome + Diabetic + FoodInsecure +
Uninsured + DrugOverdoseMortalityRate)
Residuals:
Min 1Q Median 3Q Max
-5.4550 -0.8559 0.0309 0.8038 7.1801
Coefficients:
Estimate Std. Error t value Pr(>|t|)...

Residuals:
Min 1Q
Median 3Q
Max
-6249.5 -382.9 -139.3 25.6 31164.7
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.311e+02 2.219e+02 0.591
0.5550
debt 1.283e-01
3.288e-01 0.390
0.6966
sales 2.942e-01
1.366e-01 2.154 0.0321 *
income 1.546e+01
2.697e+00 5.730 2.42e-08 ***
assets -2.390e-05 4.839e-03
-0.005 0.9961
seo
2.973e+02 2.627e+02 1.132
0.2587
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’
1
Residual standard error: 2019 on 303 degrees of freedom
Multiple R-squared: 0.258, Adjusted...

Below is the R output of a study of ACT scores for the first
year of college students. This helps to see if the test scores can
predict a GPA. Simply put, this ACT helps to be an explanatory var
and GPA would be a response var.
Call:
Im(formula = GPA ~ ACT, data = gpadata)
Residuals:
Min 1Q Median 3Q Max
-2.74004 -0.33827 0.04062 0.44064 1.22737
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.11405 .32089 6.588 1.3e-09
***...

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