Research question
Inference for Linear Regression in R
Jo Hardin
Professor, Pomona College
Consider possible research questions for the Starbucks data
- Are protein and carbohydrates linearly associated in the population? (two-sided research question)
- Are protein and carbohydrates linearly associated in a positive direction in the population? (one-sided research question)
head(starbucks)
A tibble: 6 x 6
Item Calories Fat Carbs
<chr> <int> <dbl> <int>
1 Chonga Bagel 300 5 50
2 8-Grain Roll 380 6 70
3 Almond Croissant 410 22 45
4 Apple Fritter 460 23 56
5 Banana Nut Bread 420 22 52
6 Blueberry Muffin with Yogurt and Honey 380 16 53
# ... with 2 more variables: Fiber <int>, Protein <int>
summary(lm(Carbs ~ Protein, data = starbucks))
Call:
lm(formula = Carbs ~ Protein, data = starbucks)
Residuals:
Min 1Q Median 3Q Max
-35.360 -11.019 0.125 9.970 35.640
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.1116 2.4680 15.04 <2e-16 ***
Protein 0.3815 0.1734 2.20 0.0299 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
...
lm(Carbs ~ Protein, data = starbucks) %>% tidy()
term estimate std.error statistic p.value
1 (Intercept) 37.1116401 2.4680349 15.036919 1.539345e-28
2 Protein 0.3814696 0.1734226 2.199654 2.990434e-02
Call:
lm(formula = Carbs ~ Protein,
data = starbucks)
Residuals:
Min 1Q Median 3Q Max
-35.360 -11.019 0.125 9.970 35.640
Coefficients:
summary(lm(Carbs ~ Protein,
data = starbucks))
Std. Error
2.4680
0.1734
Estimate Std. Error
(Intercept) 37.1116 2.4680
Protein 0.3815 0.1734
t value Pr(>|t|)
(Intercept) 15.04 <2e-16 ***
Protein 2.20 0.0299 *
--
Signif. codes:
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
lm(Carbs ~ Protein,
data = starbucks) %>%
tidy()
std.error
2.4680349
0.1734226
Call:
lm(formula = Carbs ~ Protein,
data = starbucks)
Residuals:
Min 1Q Median 3Q Max
-35.360 -11.019 0.125 9.970 35.640
Coefficients:
summary(lm(Carbs ~ Protein,
data = starbucks))
t value
15.04
2.20
Estimate Std. Error
(Intercept) 37.1116 2.4680
Protein 0.3815 0.1734
t value Pr(>|t|)
(Intercept) 15.04 <2e-16 ***
Protein 2.20 0.0299 *
--
Signif. codes:
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
lm(Carbs ~ Protein,
data = starbucks) %>%
tidy()
statistic
15.036919
2.199654
Call:
lm(formula = Carbs ~ Protein,
data = starbucks)
Residuals:
Min 1Q Median 3Q Max
-35.360 -11.019 0.125 9.970 35.640
Coefficients:
summary(lm(Carbs ~ Protein,
data = starbucks))
Pr(>|t|)
<2e-16 ***
0.0299 *
Estimate Std. Error
(Intercept) 37.1116 2.4680
Protein 0.3815 0.1734
t value Pr(>|t|)
(Intercept) 15.04 <2e-16 ***
Protein 2.20 0.0299 *
--
Signif. codes:
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
lm(Carbs ~ Protein,
data = starbucks) %>%
tidy()
p.value
1.539345e-28
2.990434e-02
Let's practice!
Inference for Linear Regression in R
